Starting RVing with a PUP behind a minivan - thoughts?

So, in about 2 years, we're doing a family trip (myself, DW, and 3 younger boys, in the 7-12 y.o. range at that point) from West Coast to East Coast and back again - up to 2 months in total (exact route plans haven't been decided, just the end points). We had originally been thinking about doing it as a train trip, but we just realized that it would be way more fun to go camping across the country. My DW and I are both fairly experienced campers (both tent and RVing), but we haven't owned our own RV before, so we're looking for some advice on getting started.

We currently own a 2011 Dodge Grand Caravan Mainstreet, which has a towing capacity of 3600 lbs, but does not have the tow package, so no hitch or wiring at the moment.

We were thinking we would like to get a small PUP trailer large enough to sleep 2 adults comfortably, and sleep all 5 of us occasionally (the boys'll be tenting it the majority of them time, with exceptions for bad weather and such), as that should be light enough to be towed by the minivan, allowing us to skip purchasing a dedicated TV for the time being. We could spend up to about $10,000 on the entire setup (and looking to buy around next April or so, which would give us a summer to get used to the setup before hauling off across the country with it).

So, in summary, our current (newbie) plan: Purchase a used PUP and add aftermarket tow hitch and wiring hookup to the Grand Caravan, and take it across the country and back.

Is this within the realm of sanity? :)

If so, does anyone have recommendations on the PUP, the aftermarket hitch, the aftermarket wiring modifications, etc.?

If it's not sane, does anyone have recommendations on an alternative solution that will total around $10,000 (maybe $15,000 if it's really compelling), sleep 2 adults comfortably, and can sleep an additional 3 mid-sized boys in a pinch?

Thanks!

-James