Look, I get the student loan thing. I'm 36 and still paying mine off. Thankfully, we now have good incomes and can pay them down in a reasonable amount of time. My husband paid his off last year. I think living in an RV to save money with 3 small kids sounds like a terrible idea LOL.
What about selling the house and use the profits instead to pay off/pay down the student loans, and rent an apartment/small house while you save up to buy another house/pay off the rest of the student loans? I'm not super familiar with rental costs in Alabama but how much could a 2BR apartment cost? We have friends doing what you are doing (sold the house to save money etc), in a 2BR, and their kids are older than yours, and they homeschool. The kids are happy and they live in a nice family-friendly apartment complex with a pool, playgrounds, and a dog park for their dog.
As previously mentioned, RVs depreciate at a very quick rate. Example, our first trailer, a nice 32' bumper pull toyhauler, was purchased new at around $34,000. Less than 3 years later, we traded it in for $20,000. We could have maybe sold it on our own if we waited long enough for a few thousand more than the dealer offered.
So sure, the lot rent of $425.00 sounds appealing, but as mentioned, think of the other costs involved. Laundry costs. Heat costs, as RVs are not well insulated, even the "4 season" ones. Higher grocery costs since you can't buy in bulk when things are on sale. And, of course the money you lose in depreciation every year, that's a huge "expense".
The last thing to consider is who your neighbors might be in a long term RV park that is only $425.00 a month. I know the ones around here, some of the folks that live here are not who I'd want my kids growing up around.