My grandparents traveled with their three oldest children in a Model T touring car from western Montana to the PNW, down to Calfornia, and across the South to Georgia and Florida before moving north to Ohio, and eventually Michigan.
Not a RV trip, it was more than several years, long enough for the oldest to finish school, the last two to be born and reach school age. The trip was about finding work for the family during the Depression: planting, harvesting, cutting timber, building roads and railroads, building barns, sheds and houses. Shelter on the road was a tent or fly attached to the car, at work sites it was what the employer provided or what they could quickly build.
Full timing, but not RVing. Not camping. It was about making a living for roughlya decade of the Depression. Neither of my grandparents ever drove, it was something the youngsters took care of.
Many people still do this, I meet them in municipal or county RV parks in the parts of the country where work is hard labor and temporary. Whole families, now usually a couple cars, and some type of RV, maybe even two, converted to permanent living.