Just to clarify things a bit. I fly long haul to New Zealand once a year with kids (now 7 and 18months)
Exit seats, by airline regulations, must be given to someone who is adult and physically 'able'. They are not expected to open doors or perform any duties in event of an emergency. They are simply expected to follow instructions. However as they are, obviously, in the exit row, they need to be able to move fast and respond quickly in case of emergency. I have actually been moved from an exit when I sat down with my child who was 4 at the time. Lots of apologies made, but a mistake had been made when I was allocated seats. A child is simply not permitted in an exit row, and the airline staff are allowed to move anyone from an exit row if they consider that they may cause an obstruction in an emergency.
Bulkhead seats are those facing a wall, as opposed to facing another row of seats. They are where the cots are fitted so obviously they are given to those with babies first. It is not true that they have more leg room. In some instances, yes they do, but as you cannot stretch your legs under the seat in front, they actually have less leg room in many cases. However they are ideal for kids as kids can stand up and move around (as they do!) without disturbing the person in the seat in front. Anyone who has enduring a flight with an active child in the seat behind them will understand what I mean. For the comfort of other passengers it is therefore preferably that kids are seated in bulkhead seats. Bulkhead seats can be booked in advance, or requested at checkin, but you will be moved if someone requires the use of the cot.
I hope this clarifies the issue. Please note that most of us realise that travelling with young children is not ideal. However in many cases it is simply unavoidable.