In an emergency I'd be willing and able to operate the doors but if the children were with me then I would have a full time job dealing with them so it's fair enough that infants/minors aren't allowed in these rows.
Never tried to get an exit row on BA with the kids in tow but my experience of Ryan Air (yeah, yeah

) is that they won't let you sit in the exit rows with children either. I asked a couple of times because I'm normally the first to board when travelling with the kids but they say choose any seats except the ones with yellow headrests (exit rows).