The solenoid is called the TCC (Torque Converter Clutch) solenoid. It's there to lock and unlock the TC. Like I said if this is your prob, its right on the valve body when u take off the pan. So its easy enough to swap out.
The TCC is the dark round object above the pink paint. When you take off the pan its easy enough to locate really.
I would take it to another tranny shop for more opinions though, instead of just throwing parts at it. Maybe they can confirm what problem you're having through tranny codes. Swapping the TCC is easy enough, but you would need a new one and new fluid.