Well, it will be the kids check-in in their bags, not you. Airlines do not expect small kids to pack their bags themselves, and, as the dad will be at check-in with them, it is understood that their guardian or parent supervised the packing. But you will be checking in your own bag and the children theirs.
Anyway, if someone says they are carrying something they didnīt pack themselves, the procedure is usually just taking the bag to a special check-in desk, and the bags will undergo a more scrutinised and separated security check and x-ray scan.
Is not illegal to carry something you didnīt pack, it just has to go through different channels, and the usual outcome is just the inconvenience of having to take the bags to a special desk (in LHR is usually the belt for outsized luggage).