A man who can't hang out with his guy friends because he can never get a babysitter for his kids. Particularly in a suburban area where the guys only get to be without their wives a few times a year.
"Tom is such a dadsitter. Us guys hang out twice a year, and he can't find a babysitter once in a while?"
"Hey guys, I can't go out to the bar tonight, I'm a dadsitter"