familiar controls replaces values +1 per trip. does that mean i can put omega batman in the batmobile and keep him in there until the batmobile is wrecked and it keeps his values +1

No. When you replace the Batmobile stats with the pilot's, Familiar Controls just makes them +1. But it only lasts until your next turn when the pilot takes the click of damage.

Also Omega Batman doesn't qualify as "batman"

well we've been playing it wrong lol... thanks dude

But he does have the Batman Family keyword which makes this Abili-trait usable.

However, the BATCOMPUTER Abili-trait couldn't be used with him, since it's based on the characters name.

The fact that the stat swaps only last until the beginning of your next turn isn't explicitly stated on the card, it's something we've been passed down from the oranges. So don't feel too bad.