How many miles are on it? What is the state of maintenance? spark plugs? wires? fuel & air filters? has anyone checked the fuel pressure? Has the check engine light been on? Do the mechanic(s) ever mention anything about scanning the computer and if so, what - in particular - was found? Do you have any error codes recorded on any of the paperwork from them? (These would look like “P0123”).
Without knowing about all of that one thing that would fit would be a torque converter clutch that is stuck on. That’s likely where the idea of rebuilding the transmission is from. Is the “garage” actually a transmission shop? While good general mechanics can do most of the work on most any car, transmission knowledge and work is pretty specialized. So I’d ask around and find the best local transmission shop you can and take it there.