Checked-out teenagers

It doesn't mean dead [as another user's answer, now deleted, suggests], except metaphorically. It means uninvolved, uninterested, tuned out, unresponsive.

Given the context of the rest of the sentence (clue: "bitchy wife"), I would interpret "checked-out teenagers" to mean that his kids are disengaged from any meaningful family interaction and he is using that general assessment of his family life to justify his current course of action.

Urban dictionary records usage of checked out as:

"someone who doesn't care about their job anymore and is about to quit."

The children are most likely a care-free, non-committal teenagers who are not to be relied on for anything much.