I have an '03 Dodge Cummins Dually 4X4, when I put it in reverse my gas pedal gets hard to push and then after I put it back in drive, the transmission doesn't seem to shift right. Any suggestions or ideas?

 

explain your shifting problem. Band adjustment sounds like to me Might want to make it a full flush, filter change and band adjustment. Unless it is haunting 1-2-1-2 shift if that is the case gov. solenoid also.
or just plain out slipping REBUILD.
As far as the hard pedal in Reverse news to me I've drove as fast as i can in my truck before the pedal went to the floor but stops at a set rpm so i might have done 10 mph ish in reverse. I wasn't look forwards so I didn't see how fast i was driving.