Also buggies, car seats etc are all free (not included in the weight allowance). Emirates are the best of the bunch in terms of the Middle East carriers so tell Jamie not to be afraid to ask for help. In Dubai they provide buggies at the gates that you collect on arrival and dump just before boarding the next flight. If she arrives from London at the A gates (most likely) she will need to catch a train to the B gates, no harm in her asking for them to take on the back of the cart with the kids between gates etc, I am sure they will oblige.
I don't think they will allow her to add the carry on to her baggage allowance. A lot of the airlines have setup systems which don't allow the check in assistant to accept excess baggage without charging (I know this the case with most european carriers now).