Wow...thanks for all your interpretations!
That the monster is a kind of Frankensteinish golem stitched together from bits and pieces that you have nonetheless been able to tour around with reflects the fact that you can get along with your dad and have halfway decent times with him, but his identity to you -- your relationship to him -- is fragmented and artificial and chimeric. It's not "normal" and you don't know what to make of it.
I see the monster and "me" in the dream as two sides of me. The monster is the part of me that didn't get a lot of the basics (social skills, love, self-esteem) and cobbled together what he needed from books, TV and imagination. It wasn't pretty and didn't work very well, but was rather heroic and even kind of sweet.
"Me" is the adult everyone sees--not polished but passable. Sort of detached, loves solving problems, doesn't really connect to the problem. Doesn't hate the monster in the car, but doesn't quite identify either.
You are lonely except for these monsters. (I just read another of your posts).
Interesting...I think you're right, Puffer. We're really only connected to the things we're struggling to disconnect from.
Blueshift--I agree about the symbols and feelings... Not sure about the detachment now--is that a goal? Or something to try to get past? (I'd been very depressed when I had that dream and detachment seemed great. Now, I think I'm ready for some connection again.)
TW -- Monastery/monster. That's cool. Now I'll have to sleep with a Thesaurus by my bed! (I used to dream about elevators a lot...must have been elated.)