Good afternoon.
Get your car out of there to another shop that is honest.
A good shop will tell you the process of diagnostics. It does sound like you have a transmission issue but it needs to be removed and inspected before anyone can give you an idea of the failure and the cost.
This will not be cheap by any means. Any shop that wants money up front for a repair is not a shop you want to deal with.
Roy
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Thursday, November 8th, 2018 AT 2:36 PM