Considerations:
1. Your son is a lot older than your daughter. An RV will be very tight quarters and the "closeness" may be annoying for him and stressful for you.
2. Living in an RV is NOT going to be cheaper than living in an apartment. Your expenses will be different, but the total amount will not be much better.
3. Your daughter still needs to attend school. If you homeschool, then the 3 of you will be home in the RV all day every day. Again, that can be annoying for your son (who likely enjoys his privacy) and stressful for you (having to deal with his annoyance and your daughter's hurt if he doesn't want to spend time with her). If you send her to school, then you're tied down to a single location for the school year. Finding an RV park near a quality school could be difficult - so you may end up having to drive her across town every day.
Why not step back and consider doing a summer trip this year? That will get you out and away, give your son a great "grad year summer trip", and give your daughter a break from the same-same routine. You could try camping? Or do a road trip in the Yaris and stay at inexpensive hotels (Days Inn, Quality, etc.).
