I'm late with response, but may be this post will be helpful for other readers in same situation.
I'm ukrainian, I had a wedding in ukraine few years ago so i know what I'm talking about. But ukraine is a big country, so traditions may vary.
At big cities as Kiev, weddings are less traditional as at small cities.
Usually its short ceremony in city hall, then longer ceremony in church (2-3 hours), and then big party in restaurant (6pm till midnight or longer)
Banya at parents house is not a part of this.
I think this is just the way parents want to meet you, show something different, what you didn't see before.
As other people said, the best present for parents will be bottle of alcohol (american whiskey is good) and perfume.
Alcohol is not for drinking at that same day, its more for their bar collection. Also, do not forget flowers for mom, odd number (3 or 7 or 11...)
Its funny when people think that ukrainians or russians love to drink vodka. Its not exactly like that. Its more tradition, when people having visitors or guest, when hosting some party, they usually drink. Alcohol making people more relaxed. Whiskey or rum or other alcohol is new for "soviet" people, so thats why they prefer vodka. Women usually drink wine instead.
Also, they are not mixing vodka with juice. They are doing shots. So its may look weird to them, if you will mix it. Learn how to do shots, but do not do more than 3, if you are beginner.
Less than 3 shots may be disrespectful for host, more may be difficult for you. Learn how to say NO, when they will ask you to get more. And they will )))
Now lets get back to the actual wedding.
1. Ceremony in City Hall.
It is the place where newlyweds will exchange their rings and sign "wedding papers"
Its usually short, 30 min to 1 hour.
Guest are usually doesn't do any actions here. Just watching ceremony, taking pictures.
Not all guests are coming here, only close friends and relatives.
2. Church (I'm talking about orthodox wedding)
Guests also does not doing anything but watching. Maybe you will need some small bills as a charity to church ($5-10).
Women should have their heads covered. Otherwise they can wait outside.
Ceremony is boring, guests need to stay calm, watch and listen. No cellphones or other electronics are allowed.
Ceremony can take 2-3 hours. So guests are usually doing outside brakes.
This are pictures from my ceremony
3. Party at restaurant (or at home, if its big enough)
This is a place where all fun begins. =)
All starts with meeting all guests personally. Guests giving their presents and wishes.
Alot of people just giving cash in nice envelopes and postcards. Some may present some things for home, such as some electronics or kitchen supplies.
Usually at this point each guest taking a shot of vodka or glass of wine
Party is different from american parties. All people are usually having sit at the table, there are a lot of food there, so everybody are free to chose what they want.
There usually is some entertainer (tamadah), who can make some jokes, start some games or ask some people to give wishes. But usually this is just eating and drinking.
In between this, there are breaks with dancing, more games, traditional things, etc.
Usually it is 3 rounds with 2 breaks.
All this may include stealing a bride or bride's shoe, washing mother-in-law foots, etc.
A lot of fun.
Here are some pics. You can look what people wearing, to have an idea.
P.S. People in ukraine are not always smiling, but it doesn't mean that they are angry or sad.
P.S.S. Some people may be too drunk by the end of wedding, be aware of it.
P.S.S.S I hope this post will help somebody