The problem with the transmission shop is that they can get $1500 for a rebuild, but only $80 for the part you need. If they are doing a flush & fill already, then they can put the solenoid in in about 15 more minutes. Take the pan off to drain the trans. There is a filter kit that is needed. When the pan is off, there are something like 8 screws that hold the valve body where the solenoid fits. You take these screws out, replace the solenoid, and put it all back together. If they charged $175 for a flush & fill with a new filter kit, then they should drop in the solenoid for the cost of the part and _maybe_ another half hour of labor. Personally, I could make an argument that they do it for the part because they are already charging an hour of labor for a job that takes less than an hour to perform, but giving the shop the benefit of any doubt, it is fair that they get a half hour for the extra work.
The hard part is that you have to stand on your head spitting wooden nickles doing a Russian tap dance while filling the transmission fluid again. There is a specific method of filling that I don't know, but they make it sound difficult to do while laying on your back on the garage floor. The shop can do this easily because the car is 7 feet off the floor, and this job is far easier when standing than when laying on your back.