The great thing about having a 2" receiver is that one can set up different mounts and quickly switch between them. I use the flat bar shown above, a hook, a clevis, and one set up with a 2" ball one one side, 1 7/8 on the flip side. I use them on the truck, Mule, and Kubota tractor. I've found them at yard sales mostly. Very inexpensive that way.
Pin sizes.... you'll have to measure the diameter of the holes on the cart side to get the right width pin. I think mine is 4"-5" long with a large handle and I find I don't need to put a cotter pin to keep it in place. The hole on the receiver mount is larger than the cart holes will be. As frugalangler mentioned, it will have a lot of slop in the fit, but unless you'll be on the highway with it, it should be fine.