I'm going to answer for those who have inflexible teens/spouses/kids. First of all, I am from a military area so please know that if anyone knows something about frequent movers, it's me.
Key Point 1
Children are not inherently flexible and adaptive to change; this is a personality trait. There are geriatrics who love change and 9 y/o's that hate it. Introverts tend to dislike change more than extroverts, but there's no hard and fast rule.
Determine what type of child yours is. Were they flexible and sociable as a child, or were they bashful and standoffish? Have they always made friends easily? Or not? Are they private or fairly open? Are they adventurous eaters or stick to a few specific foods? Do they have to like the activity to participate or can they derive some enjoyment from an activity that is not their first choice? Or, in other words, are they like Shelden or Penny? LOL
If you're moving someone who has never been good with travel/change in scenery, who has a list of things they won't eat that's longer than the constitution itself and/or who has a hard time making friends, then you're essentially asking them to move a mountain. Now, you might be saying, "Is it THAT hard to say 'hi' and give someone a chance?" Yes, yes it is to some of us. We are not good at it and we're admittedly selective - sometimes to a fault - in picking our friends and our food. You may want to offer assistance in the form of letting them go online and choose some sort of activity ahead of time to participate in.
I'm an extremely private person. Private people have the reputation being "hard to trust", "standoffish", "snobby", "judgmental", "Hard to get to know" - and a lucrative array of other negative adjectives. Open people - you know - the girl who jokes about her girl stuff, and is more than willing to talk about her latest medical appointment, the time she accidentally wet herself laughing, her past, has pictures from their entire life displayed in their bedroom or who is always willing to dance...are seen as more approachable and fun.
Admittedly if you don't share much about yourself for privacy reasons, people won't get to know you, and if you continue this for longer than a month, they tend to drop out of your life. They may have confessed everything under the sun to you, but if you say nothing to them, you're a counseller, or an impersonal doctor at best. You are extremely trustworthy, clearly but there's not bond as "Friends". You will find that you have a lot of people come to you for help but no one who will invite you over for dinner or to hang out because you've established a professional relationship and they know little to nothing about you on a personal level. They can't help you like they want to.
Now, maybe you/your teen likes this. I like this 93% of the time, but do wish I had more friends to spend time with 7% of the time.
If your teen is like this, you might remind them that they have full control over what they share with others, but if they're not going to open up and let people in, don't expect people to stick around or come to them. Don't take it upon yourself to others about them; it won't be interpreted as "helpful"; they won't think: "Well, gosh, now that mom told them I'm distrusting because I was abused, I guess I can be friends with this person." Nope. Instead we push that person even further away - even if they're sitting there with open arms telling us it's okay - and ALL trust is absolutely demolished between you and them. ***
*** Abuse and trauma are serious. Sexual, physical, verbal and emotional abuse lead to PTSD often. Negligence in early childhood, or feeling unwanted before the age of 5, is a permanent mark that leads to abandonment issues. They don't go away; they are managed with treatment that includes medication and counseling. I used a very harsh example. I can't tell you why we do this; it's very complicated to us, as well. ***
How do you know if your teen is fine with it? Well, if they're still getting good grades, attending to hygiene and aren't sleeping excessively, sharing suicidal thoughts, self-harming or irritable, then their probably fine. If you ask them, "Don't you want to go to sr. dance with that boy down the street who asked you?" And they answer back: Nope. I hate dancing (assuming they do), i'm not wearing a stupid dress and it's too loud, with a smile, and then go back to their computer, they're fine. They're introverted geeks.
If you notice signs of depression, seek help medically first, then worry about the social aspect.
Are they stubborn to a point of hindering themselves knowingly?
I'm this person. I don't care to travel much - unless it's camping or I like the place otherwise. I don't make friends super easily but I'm incredibly nice, and easy to talk to, people tell me. I work in nursing and am often the one patients will confide in - but of course, you really *shouldn't* be friends with your patients.
If they're being angry because of whatever reason they're not telling you, (probably a combination of lack of control + not liking change + perhaps mental illness +/- low self-esteem/poor self-image + issues with the family unit), then you can't do a whole lot for them except remain open if they decide to talk to you. They're obviously pissed at you now, though. You can't tell them HOW to feel, but you can tell them what isn't acceptable within reason. Cursing at people and punching siblings isn't acceptable; saying you don't like something in a polite enough way, is acceptable.
You can't change WHO they are, but you can guide them to being more tactful, likable, quieter, or whatever it is they might need to work on.
I'm an introvert who doesn't spend time with excessive talk. I'm going to be brutally honest if you ask me my opinion or involve me in something I don't want to talk about.
Over the years, I've become much better. I'm still blunt but it's more tactful.
You can't change who your child is, but you can guide them to be professional in nature. When I had to move to a new place, I just didn't try to meet anyone. I wasn't outright mean but I never spoke to them, never checked on them if I heard something, never asked or accepted an invitation anywhere. I worked and slept. I didn't go out much except to TGIF alone by choice, for their Jack Daniels' steak (which I miss now, but i have high cholesterol!)
Eventually, after 6 years, I was able to move back home. I didn't have any friends from the place - save for one from work. I didn't try to meet anyone romantically. I happened to date one girl who was a good match, but when she told me she planned to be a female-doctor, I told her I couldn't support that career choice for a woman, as nicely as I could.
My brother on the other hand, still has friends he sees regularly from college and everywhere he's lived. So, it just depends.
If your teen doesn't like the new school and after some time of trying to fit in, can't, try to find a different school. Look, maybe your teen benefits from uniforms, maybe they're good at online, maybe they're just generic public school kids like me. Maybe they need a magnet school or even community college classes. Try to find a school that works for them.
I know that some states have horrendous (Hawaii!!!) school systems. If you absolutely can't let them go into the school they want, then at least explain to them the reasoning behind it. I know some states have overall great school systems. Education is VITAL. It has to be good.
If your teen is simply doing stuff to make it clear that he isn't happy and isn't trying to make it better/have a better attitude, then set your reasonable limits and let him be. Don't feed it by giving him negative attention if you can avoid it. Continue to give praise lightly when able - even if they reject it - and always extend the same offers to them as you do your other children - even if they reject it angrily. It'll only add fuel if you stop offering it. If you decide to sign them up for an activity to get them out of the house and make friends, don't spend money. FREE stuff.
When they have a better attitude, and can tell you reasonable ways you can help them, do so. They probably don't need a new car, for example, but maybe they would like some new clothes that are more trendy to help them fit in, or maybe they just need to know that they're not betraying anyone by enjoying this new location.
Did they love their teachers? Really like their doctor? Were really close to their best friend? Do they feel they are betraying them if they adapt and enjoy this new place and new people? Did they promise that one special person they'd never date anyone else, wouldn't do a specific activity without them, would go to the college as them? If possible, have those people tell them they're not betraying them by choosing a different path, for whatever reason, but if not possible, reiterate that yourself. Remind them that even if you moved back home in a year, things would be different.
They may truly have disdain for this place, too. Remind them that once they're gainfully employed they can move to where they would prefer.
Most kids use social media so that should help too. However, if you don't allow social media (good call!) or you are like me and avoid that toxic crap, you may find yourself cut off from the world. I missed the memo that said you were a creep if you didn't give Mark Suck-erburg your personal info so that he could sell it to third parties without second thought. I find that people don't want to text or email - they want to "facebook" and see my pictures for some reason. So, that's something to take into consideration. IF they'r not into/allowed on social media, maybe make sure they have their own Total Wireless flip phone and enough minutes to chat with friends at home by video or talk?
Good luck all.