4 in a cabin seems a bit cramped to me - and only one bathroom! Check the config as some rooms have upper and lower berths and children under 6 are not allowed on the upper bunks so it means SIL will have to sleep up there. Go for 2 cabins if you can possibly afford it. As we have no idea about you it is hard to suggest who to sail with - personally I would go with a newer American ship for the pure wow factor, better service and great amenities. There are people on this site who will tell you go go with OV or P&O (which are ghastly IMHO). Best thing to do is to go to the highstreet and take all the cruise brochures from your local TA shop and see which one appeals. BTW RCI are generally acknowledged to be the best cruise line afloat for children.
If you do go to high street TA to gather brochures, I would then suggest you actually get any further info and advice from a specialist cruise agent such as cruise co uk as often I find the high street TA really do not have enough knowledge to give good sound advice on cruising. As for actual choice of cruise line, I would stick to RCI, Carnival, Celebrity, but it does depend on whether you want formal or informal cruising and also what itinery as there are many caribbean islands to chose from. Personally I would have on my must list St. Thomas, Tortola, Antigua.
Just to add, ref your question on cabin configuration: If you all want to share (4berth) bear these factors in mind. Usual Inside and outside configuration for 4 berths is two ower and two upper berths. Balcony cabin is usually twin plus a double sofa bed. I think Aldrich suggestion of two cabins is the best option.