Hi,
Clearly the transmission engaging and parking brakes have nothing to do with each other so I think the best thing to do is lift the rear drive wheels off the ground with a jack and jack stands, then put it in gear and see if the wheels spin with no friction on them. If not, then we need to remove the drive shaft and see if the output shaft of the transmission spins when you put it in gear.
If the output shaft spins with no drive shaft then we know the issue is in the rear end.
If the output shaft does not spin then we know the issue is in the transmission. At this point we need to find out if the parking pawl is releasing or not.
In fact, I attached a recall notice to the thread that talks about this part. The recall is for it not holding it in park at times and yours may not be releasing so it doesn't match exactly but that doesn't mean getting the recall done won't fix your issue as well.
I would suggest calling the local dealer to see if this recall is outstanding on your vehicle and if it is, just have it performed to see if you can get your issue corrected as well.
Let me know what you find and we can go from there. Thanks
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Tuesday, May 4th, 2021 AT 9:39 AM