Transmission noise and won't go into reverse

Note: I recently had this same problem and had the transmission replaced. I'm having the same problem less than thousand miles after, and fortunately it is under warranty. But I now suspect something may be going wrong with the computer and it's communication between the engine and the transmission, or possibly there's something else that is causing this, and I want to find out more before I take it back to the shop.

The first time I had this problem I pulled the car into my new driveway and it was making a strange noise as I pulled in, but it's a two track with possible branches it could have picked up, and I was just moving in so I thought no more about it.
The next day when we went to back the car out it wouldn't go into reverse. The tow truck driver had to drag it out of the driveway because the wheels were locked.

I took it to the shop and they said, yes, the transmission is bad and they got me a low mileage tranny and installed it. Last week, after a few weeks with the new one, we drove it about 400 miles up into the mountains for a camping trip and all seemed well. But as we were getting ready to leave I started hearing that weird grinding sound again. The next day we packed up to go home, and as we went forward I was hearing the grinding noise again, and the car didn't want to get up speed in low gear. Once it shifted up it sounded and drove fine, so I decided to try to drive home.

We stopped in a rest area, and we weren't able to back out, or even push it backward. Fortunately we were able to move the concrete barriers and go forward so we could get back on the road. Again the low gear sounded terrible, but it was fine once it shifted up and we were able to make it home.

Here's something I left out of the story because I wasn't sure it was related, but now I suspect it may be:
For a while, maybe a year or so, the car has been shifting hard. In other words, making a clunking sound and jerking when it shifts. It is intermittent, and I was hoping that would go away with the new tranny. Since it didn't go away I mentioned it to the shop and they said that "was normal" for an old Camry. I said I wondered if it was a linkage between the engine and the transmission-that something wasn't communicating when to shift, hence causing mis-shifting and the clunking sound. By then it was really loud and jerk-y. I was suspecting the mis-shifting could cause the gears to be misaligned and then to make noise and ultimately to lock up. She said the computer tells the tranny when to shift so it she said it couldn't have anything to do with it.

But now I suspect maybe it does, and I would love to hear from your experience what could be going on. If I need a new computer, or if something else is causing this. The tranny is under warranty but I don't see any sense in replacing it without resolving the issue that is causing the problem. Since they are identical scenarios I doubt that this is coincidence.

Thanks for your time!
Pat