Ditto X2 on the MH. Been there done that and MH is the way to go.
Take off RV'ing without towing a car.
I full timed for 2 years without a toad. There really is not that many places site seeing that you can't take a MH to. Most have parking for RV's. Going into town? I haven't seen a MH yet that didn't fit in a grocery store parking lot.
Later on find an inexpensive used lightweight car to tow. IMHO too many people think you have to go out and buy a brand spanking pricey new toad to go RV'ing. I bought mine with full intentions of it being just a used car to tow around if I needed it and selling it when I was done full timing.
RE: your idea on a truck with bed cover for the dogs.
Dogs in a covered truck bed will heat stroke dead in seconds in summer and freeze to death in winter. RV'ing this way with dogs will be your biggest problem and ruin your RV'ing time with the family.
Just saying. Good luck finding just the right RV for you and your family.