never skimp on the tow rig. get one with plenty of room, brakes and power (in that order). Don't even consider a Jeep / similar.
You need BEEF, BRAKES, and LONG wheelbase.
Sounds like you should do a 'skoolie' and run it on free cooking oil, tow a small economical SUV toad (Suzuki with an evil VW diesel transplant). This would be affordable and doable, but a bit of a hassle / maint concern. The Skoolie would give you S-P-A-C-E and a ratty interior for the dog/kids to roust around in. It is robust and will safely tow your toad and there are some delightful conversions VERY cheap (usually unfinished). I saw so many excellent commercial bus / truck / skoolie conversions in NZ that had been used for several decades. Look at pics and blogs. Consider something with a DT466 engine, they are good service, tough, economical, and LOTS of parts / repair / service. Hopefully.... it will never break down! I much prefer Air Brakes, but you will want to add an endorsement to your Driver's license, and get a tutorial.
Add extra door / exits especially for DH and dog/kids. One is TOO FEW exits. Add an awning / attachable dining area / pet/kids playground.
Wood stove with cooking / baking will keep you toasty and well fed. (cheap)
A traditional RV would get pretty hammered doing a long trip 'living' with pets. Not worth the wasted $$ to trash and maintain a traditional RV.
Your DH will THANK YOU for preserving his 86 GMC so he can use it the rest of his life.