How to best splice wires together?

I agree. Even if soldering is the better solution, is it really worth it for the OP to learn how to solder and buy the equipment just for this repair? If we were talking about an old fashioned butt connector, and the OP planned to keep the trailer for decades to come, maybe. If we are talking about a crimp solder seal heat shrink butt connector, I wouldn’t bother learning how to solder and buying the equipment, especially since the dog will probably just chew it up again.

I wish I could solder. I used to watch my father do it when I was a kid. Now I am not allowed to solder because of my pacemaker, which would make the crimp solder seal heat shrink butt connector the perfect solution.