Which kind of RV to buy for our situation? Details...

If her budget is limited and under $10,000, it isn't going to be helpful to rent. Renting for a week will take out a good chunk of her budget.

I would look at costs of RV Parks. I wouldn't try to stealth camp with my daughter in one city/town for a year or more. Just seems to be sending the wrong messages to her (e.g., it's illegal but we can do it, as well as, you're important but not enough to put money out to do it legally).