What brand of trike are you getting? I have a Evelo Compass eTrike that I bought for my wife. It has a mid drive motor and it works quite well. That said, it seems to me that converting a non powered trike to a mid drive motor would be quite involved. I have seen some trike conversions using a hub drive on the front wheel, but not sure I have heard of anyone converting a trike with a mid drive.
Several years ago we had a non powered Miami Sun trike. If I remember correctly, only one rear wheel on that trike was connected to the chain. The other rear wheel was free wheeling. Also, I think only one rear wheel was braked. The Evelo Compass has a differential and both rear wheels can receive power and the rear brake is a disc brake that I am pretty sure brakes both wheels.