We have been full-timing for 5 years and we have 16 and a 19 year old girls...and I have got to say that CLOTHES take up good 90% of our storage space.
About every 3 months, the missus takes the girls thrift-shopping and they buy all new wardrobes, usually for less than about 30 bucks a head. The old stuff usually gets donated back to the same thrift shop. It is like a revolving closet that always gets restocked with new/different stuff, so the clothes stay fresh and the girls get to flex their shopping bones regularly without breaking the bank. Its a win-win all around.
Find the thrift stores in the area you are visiting and go early on whatever their regular "sale day" is to get the most bang for your buck. That is what my wife and girls do.
In the interests of being realistic (and hearing my wife's voice in my head with her degree in early childhood development and 14 years teaching experience), I would speculate that a larger problem than clothes would be toys...where most kids have boxes of toys and a yard to play with them in, your children will be more noticeably limited by the amount of room their toy box, and their "backyard" is about to become a parking lot.. Quality toys and manipulatives (duplo, erector, tinkertoy) vs quantity toys (happy meal giveaways and action figures) will need to be weighed heavily against one another if you expect children not to get bored indoors on stay-inside days and learn from playing.
To give yourself a preview of what RV life is about to be like, move into the RV for a week while it is parked in your driveway (before the house goes away) and let everyone get used to it while all the comforts of a stick-and-brick home still exist. It will make the transition easier and give you a very good idea what lies ahead of you.
Cheers!