Q: Coolant thermostat and motor mount replacement

Hello,

I live in Northern Virginia and need to have my coolant thermostat replaced (the check engine light came on and I had the problem diagnosed at a few shops). The coolant thermostat sensor is working, however each of the shops are quoting over $600 for parts and labor. After looking up the part at AutoZone, I saw that they were overcharging for the coolant thermostat (average price with sensor is $125). Is a $600 replacement cost justified? It seems that the work will only take 1-2 hours, but some mechanics have suggested a coolant flush while others have not.

Additionally, I need to replace my motor mounts because the car is vibrating a lot and very loudly. The vibrations are happening throughout the car, though I notice them more in the driver's side than the passenger side. I'm not sure which mounts need to be specifically replaced. How much should I expect this replacement to cost?

Thank you for your help.

My car has 108000 miles.
My car has an automatic transmission.