We've fulltimed for 9 years, and since I'm now in my 70s, I will be the tough minded grandma that is going to speak straight out to you.
4 kids in a small trailer - I don't think so. What might work for a 2-week summer camping trip isn't going to work for fulltiming. Realistically you need a trailer with at least a bath and a half, plus at least 2 bedrooms which will still have people sleeping in the living room, etc. A toy hauler with the garage area made into a dormitory is a better option. And none of that can be towed by a Suburban - 1 ton diesel will be necessary. And kids need 'stuff', especially when they are being removed from familiar surroundings, they need things to make them feel at home. I think you need to step back and re-think this and figure out why you want to do it and what benefit the kids will gain versus what it is going to cost them.
I will agree it isn't how much space you need, it is what your kids need. Thinking about them FIRST and FOREMOST will get you on the correct track.
Barb