Thank you, thank you, thank you, one and all.
I had a mobile RV repair guy come to my driveway and replace the whole hitch/coupler/Y-shaped piece of metal. It cost $500.
I didn't realize how bad it was. Neither me, my wife, nor my non-trailer-owner neighbor noticed it until after our 2nd trip. We're all dense...
The trailer was delivered to us from the dealer. We bought it used. The tow truck driver needed a hammer to pry the hitch off the ball when he first delivered it. I questioned this, but since I never owned a trailer, I figured maybe this was normal.
It is now fixed, and I want to thank all you fine posters for giving the advise to fix it. We took it on trip #3 of the summer, to Donner Lake, near Lake Tahoe. The hitch and ball meshed perfectly, like they should.
You may have saved some lives.