You can book pretty much any cruise through UR, you just have to call in. I did my research for cruises on the cruise line website to determine ports/price/dates and then I called into Chase to book it with UR points. They match the current pricing and promotions from the cruise line, including onboard credits, elite status discounts, etc. Something to keep in mind is that only let you apply UR points once, when you first make the reservation. Anything remaining on the balance must be paid via credit card.
I booked a cruise leaving out of Venice in October 2018 on Royal Caribbean. It cost $2000 for a junior suite (amazing deal) and I paid $800 of it with Chase UR points (roughly 53,000 points). The other $1200 will be put on my CSR closer to the due date.
As far as cruise lines, I prefer Royal Caribbean. But I am also a Diamond member, so I get a lot of perks such as suite discounts, free alcohol, diamond lounge access, etc. Royal Caribbean is a very family oriented cruise line and has a great kids club. I haven't sailed Carnival, but I know others that have and they said they preferred RC because it was less of a party cruise line and had better food. I would look generally at reviews for the child's activities to get a better idea of what your family might like.