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I could put my foot in it here and it won't be the first time but I think that the danger level of three children of that age would be very high on board ship and ashore. I am speaking personally here but I would advise waiting for at least a couple of years......respectfully yours Nei.
Frankly, it is not going to be much of a holiday - firstly the 8hr flight over to MIA, and then when on board the childrens clubs will not take the 2 youngest, the baby sitters won't accept children that young either....so you and your wife will always have to be with the children 24/7...............leave them with granny or wait at least 5 years. This is before you have even looked into the costings - most lines will charge the 3/4 passenger fare for children, the airlines will charge as well....
Your best bet would be to wait until the new Ventura is launched with P&O in April (detailed in the P&O 2008 brouchure) they are boasting some of the best child friendly facilities onboard and even have a night nursery where you could leave the infants and 3 year old (only for a couple of hours though).