IMO it's downright fraud to book a hotel for fewer people than will actually stay in the room. If OP knows that children will be traveling, it's wrong to deliberately reserve a rooms for less than the actual number of people who will arrive.

Someday one could arrive to a full hotel in an overbooked city where the reserved and assigned room cannot legally allow so many occupants. I don't see why when would want to take such a risk when traveling with children. At best one should be forced to pay the rack rate for the presidential suite or whatever high room category can officially accommodate the entire group.