Since you mention a stumble I'm going to go with some possible issues.

1) Torque converter -- when driving from a dead stop in a normal way you will feel a very strong shaking right after the upshift. Put the trans in Sport Mode and it will go away.

2) Rough Idle/Low RPM's you have a ignition issue. Check Coil Packs and plugs. The low idle is a possible vacuum leak.

I had these same problems and mine was multiple coil pack and plug failures from oil leaks around the valve covers. I think the wild card here is that I was getting a flashing check engine light showing me a misfire after a while. Prior to when this was just a nuisance it never flashed just ran horribly. I had some hoses that were dry rotting. Replaced those and finally worked out all of the ignition issues and the idle acts right now.