I'm kind of with you on this one. I just get the feeling that it's almost like a trophy sort of thing, that he's using his new girlfriend to kind of remind you of your new place in his life, and that someone else is in that spot. Sending her to take your son to feed the dogs is almost like he's trying to get her and your son to bond more, which is okay I guess. But it was unnecessary for him to pick you up in her car with her there if he wasn't out with her already and was just swinging by.
It's just too hinky.
Even just driving her car whether she was there or not. That'd be odd. But her actually being there is just too over the top.
Or maybe, from the consensus ISTP reaction, he's just emotionally oblivious and doesn't realize that anything's wrong with the incredibly awkward situations he's creating. Cause I mean... how many kids do you have? Or even if there's just two, the bare minimum for use of the word "kids" (as it's plural), that'd put you and your two kids -- three people -- in the back of the car, assuming it's a standard car that seats four people, and him and his girlfriend up in the front seat.
That's a power trip right there. That's either a blatant power trip, or it's another example of him being so inconsiderate that he's openly oblivious to common sense that three people in the back of a four-person vehicle (owned and occupied by the "new" woman in his life) would possibly be uncomfortable.
You can be logically oblivious (Feelers), or you can be emotionally oblivious (Thinkers), but it's just too hinky that he'd be an outright idiot.
Unless it seated more than four people?