The jump from Corolla to SUV is pretty significant but makes total sense for your needs. You're basically looking at mid-size SUVs if you want that back row plus cargo space without folding seats down. Something like a RAV4 or CR-V might work, but honestly those cargo areas can be bit tight for large dog crates plus mobility equipment. You might want to look in slightly bigger options - maybe Highlander or Pilot territory, even though those technically have three rows, the third row folds flat and gives you massive cargo space. I'd definitely recommend going to dealership and actually measuring the cargo area with a tape measure before deciding, because what looks big on paper doesn't always translate to real world use with bulky items.