I suspect that his Dad's truck will be much more stable towing since it is 5 inches lower and therefore the problem is most likely the OPs truck with lift and oversized tires.
Pretty well known that lifted vehicles with oversized tires tend to not make for as good of a towing rig.. This is where "Boulevard Queens" are more for looks.. Rather than heavy work..
Somewhere along the way the OP said that he tows other trailers with his truck and they tow fine. I suspect the problem is with the trailer and it would be easy to figure that out with using his dad's truck for a short tow.
