2002 Chrysler Voyager Tranny Issue?

Hello, I have a 2002 Chrysler Voyager that does a somewhat hard "downshift" when I release the gas pedal. Sometimes even harder when I press somewhat hard on the brake pedal. This usually starts after about an hour and a half of running the vehicle.

My vehicle has:
- 3.3 V6 FlexFuel
- 209,000 miles

Oh, I also found out today that I have a bad battery. It seems to reset my computer sometimes when I start my engine (I can tell this because my check engine light turns off). Could this be causing the computer to tell my tranny to do some whacky stuff?

I'm willing to buy a new battery but don't want to drop too much money into a vehicle if the tranny is going out.

Any ideas? Thanks.