Many thanks to all for taking the time to respond.
Errol, no taking responsibility - in fact he tried to blame DC1 for encouraging DC2 to run off (which may well have happened, but doesn't negate the fact that H was the adult in charge and his it was his job to keep them under control).
sparklyDMs, good suggestions, thank you. He has taken them to the cinema before because it's easy, but unfortunately I can't find any child-friendly listings near us. Suggestion of soft play did not go down well.
Quite, not driving (he'll just fall asleep on the tube). He used to, though, before I grew a pair and put my foot down. Love the water pistol idea but in practice it would just get DC2 into trouble.
Humphrey, not much use. The joys of being married to a manchild.
sooper, good question! He doesn't behave like a normal, responsible adult because he doesn't think he has to. He's a workaholic - probably due to a combination of insecurity, selfishness and emotional immaturity (his only coping mechanism for failure/adversity is to work harder/longer).
thelonggame - he might have fallen asleep but it's unlikely. He didn't deny it when I mentioned this morning that he'd only had 2 hours' sleep.
litteltabby, I'm sorry you went through that as a child. H is not depressed, just very unhappy with his lot in life (i.e. with our reasonably comfortable daily existence and family life), but I do appreciate that his lack of engagement with the DCs isn't good for them.
I left DC2 with H and went to work in the end. Being realistic, the chances of anything really terrible happening are small, and I just couldn't face the inevitable fall-out from H if I insisted on taking DC2 to work with me.
I did query with H whether he should be taking DC2 out after so little sleep, to flag up the fact that I know how late he went to bed. I also reminded DC2, in front of H, what DC2 should do if he gets lost while he is out, and also what not to do if H decides to take a nap at home. H was annoyed that I considered this necessary and tried (unsuccessfully) to cut me off.
I don't like living like this. However, part of the reason I haven't LTB yet is so that I don't have to confront this sort of scenario EOW.