Delta has no age restriction on First class. The main problem I have is when there is an infant in first and the infant is flying as a lapheld infant for NO CHARGE and I am on a paid F ticket (I had that happen this summer when I was paying to be up front DTW/SFO, mainly because I knew it was a hard upgrade and I wanted to sleep and even my Bose headphones didn't help for almost an hour). Luckilly on that trip I wasn't driving when I laned and they had plenty of free vodka on board to help knock me out
If the kids were out of their seats running around I would have complained to the FA.