Rodeo Sport Transmission Question

I have a 2001 Rodeo Sport with automatic transmission. The trans works fine at the moment, but shifts about like Grandmom's false teeth. I have read some of the threads about rebuilding and shift kits on ebay. I went to ebay and the chart of autos that the kit fit did not include my car. What transmission would I likely have and is there is shift kit for this trans? I don't want something that chirps the back tires, but something that feels like a bump instead of slide would be helpful to reliability I think.

Try cleaning the shifter control--the gizmo on the left outside that the shifter handle connects to. Remove, open, clean, reassemble and replace. Easy to do. Sometimes this alone gets them shifting right. The transmission in that is not the strongest. It's essentially the Opel Tri-Matic with an overdrive added. It's a serviceable trans, but at higher miles you can have problems. You couls also remove the pan, replace the trans filter & fluid.