Q: automatic sometimes doesn't shift on engine rev

Sometimes the car gets stuck in a low gear. We saw smoke the first time. We put in a lot of transmission fluid. It overheated when we were driving home, and filling the coolant system with water did not solve it. It turns out the car had sustained front-end damage from a previous owner (this is not my car), likely from doing something insanely stupid on a curb. The lower radiator hose was pinched so that coolant was not circulating. We fixed that, then chained the car to a pole and drove backwards to "fix" the front sub-frame damage. A YourMechanic mechanic noted on his first visit that the lower radiator hose was not re-affixed properly (which makes sense as we fixed it in a Denny's parking lot with pliers) and affixing that properly solved the overheating. The transmission portion of the problem has returned. We had to baby it home about half a mile at a time, and let the car rest overnight each time. On the lower passenger side of the car I can see possibly crushed lines.

My car has 120000 miles.
My car has an automatic transmission.