hooking up a travel trailer from the trailer's rear

I'm finding it totally incomprehensible to do what you are suggesting. Not only the impracticality of welding an A frame at the rear of the TT, but the procedure to get it out and put it back in for trips.

Is the side door in question on the right side looking at your house, thus putting the TT door directly opposite? This door swings outward?

If so, then a sensible alternative would be to make the parking space wider.

Maybe post a picture of this - I'd like to see it.