Sounds like the loose fit hitches need something like this:
http://www.hitchrider.com/hitch-vise-fit-guide-2.htm
It's about $30 and I don't know if there are any weight concerns - the weight of the load affecting how tight the device stays. There are other "anti-wobble" devices were out there but look like they are harder to use. However, this one does need a wrench to fasten the tighteners.