My battery died and now my transmission is hesitating and jerking. Why?

What is your question?

I was told by my personal mechanic that when the battery died it interfered with the computer program that oversees the transmission, causing the hesitation. (a flaw with the original program). I took it to the dealer and they said I just had a bad transmission and need to replace it. They said that they reinstalled the computer software but it didn't fix the problem, and I need to purchase a new transmission on my 5 year old car!!! It hesitates at 10 MPH, 20, 30 and 40...but runs smooth after that.