All cruise ships have family cabins. Why not talk to a cruise specialist like the freephone number at the top of the page who can advise you accordingly ......Wilba.
You have obviously been looking in the wrong places. Get some brochures and a whole new world will appear particularly if you look at Royal Caribbean Cruises where children are so well catered for, Princess and Celebrity are also very good. You will also find your answers on cruise lines web sites. ....Neil.
P&O Ventura now in the Caribbean is aimed at families and the childrens facilities are excellent with very good supervision. There are currently some good deals in the Caribbean and you fly non stop to Barbados from Manchester. As it is a sterling ship, you are not affected by the drop in sterling against the dollar.
But please do not confuse 'family cabins' with just cabins that will accomodate 4 people. On RCI you need a minimum of 5 for a true 'family cabin'. Also be sure to ask about the bed configuration - the basic cabins for 4 have both upper and lower beds and anyone under 6 years is not allowed on the upper berths which means it is where daddy has to go!