I have owned 3 96 2wd dodge ctd trucks. I have been struck in my own driveway in all of them but a few things made a huge difference.
1st buy a LS, tru-trac or buy a factory rear that has one. I have seen the 1 gen dodge rear ends with LS's sell for under $500.00. Lock rites and other lockers can be a pain in a tow rig, and you just don't need it in a 2wd. It's not like you are going to rock crawl the thing.
2nd put some weight in the bed, even when towing. I carry about 400 lbs in the bed of one of my trucks all the time and even though it is a single wheel it gets stuck less than my dually with no weight in it. When I put my camper in the bed of the dually it is incredible where it will go, so the more weight the better.
3rd. I went to a 285-75-16 geolander at tire and it also made a huge difference. I went with the geolander because it has a lot of wet weather siping and was not a extremely agressive a\t tire. (no more getting stuck on the road in the rain) You can't even hear them over the engine. I am also getting between 80,000-100,000 miles out of a set. The only problem was that they rubbed on the front. I tried coil spacers, but ended up poping ball joints every 4 months, so I took the spacers out and just trimmed the plastic on the inner fender.
Honestly none of those 3 things made more of a difference than the others, but the combination made a huge difference. Hope you get it figured out.