I prefer to over pay at the stealership so if something goes wrong I can point my finger and say "you're the only place that has ever worked on the car. In my opinion if you take it to numerous places they can always claim "someone else did it". I might be wrong in my thinking, but it gives me peace of mind. Good luck.
I don't see how they can do it for that price. The fluid change requires a kit with a new pan, filter, & gasket. The transmission pan rail will often leak if re-used. it is designed as a "ONE time on, One time off" proposition, never to be re-installed. I think they are going to re-use the pan and gasket and put in a Chinese filter. Then your REAL problems start because the oil pan and filter are integrated together. They would have to separate the filter from the pan somehow.
Here is an example... https://www.klmperformance.com/mopar-68225344aa-zf-8-speed-transmission-service-kit.html
Yea... I read reviews on local shops and asked around to buddy's that had experience with tranny shops... You don't want to mess up your tranny... Good idea asking here first though... But yea ask around...