Since I don't have to suck it up too often, I would suck it up this time and be the Dad and husband and just do it without any grumbling.
I agree completely. It seems evident that you wife wants to go enough that she says she would try to tow the trailer though she has nowhere near the experience to do that on her own. She would be operating under the same time constraint as if you went, so you should be able to plan something else for Friday evening and Saturday morning and then arrive as your friends desire. I don't see any other plan that will strengthen your marriage and your friendship. Not too great a price to pay. Unreasonable conditions? Yes. Uncomfortable for you? Yes. Family and friendship: priceless.
