The tranny doing that is not normal. My 1995 Dakota with the 5.2L did that for two years, never got worse, never got better. Up to you, I dealt with it because I didn't feel like putting $1500 for a rebuild into a truck worth $4000. It never got worse, so I guess I got lucky. Was told it was a sticky valve, but the procedures for dealing with a sticky valve didn't fix it. Stopped worrying about it when I traded it in for my Ram.
The thing about it not being able to spin the tires is probably a combination of a couple things:
1. Blown plenum gasket. Do a search using the link at the top of the page. 99% of our Dodge trucks have this issue.
Solution: Hughes or APS plenum plate kit. You should also find more info on these in your search.
2. "Death Flash". This is related to the blown plenum gasket. Again, do a search, you should be able to find it easily, as both have been re-discussed within the past month.
Solution: A tuner or custom flash. Again, you should be able to find info on this in your search.
3. 3.55 gear ratio. Most trucks came with this from the factory. A few were ordered with 3.92 gears. Off Road editions came with 4.10 gears. 3.55 gears is a decent gear for gas mileage if you have small tires (factory size 225s, for example). Anything bigger, and they aren't really a good match.
Solution: I will be upgrading to 3.92s when I have the coin to pay for the install (have the ring and pinion for both axles sitting in a box in my closet). Do a search for this as well, as others have explained it far better than I can.