If you want a full cake for the family, you'll have to order and pay for it. On the other hand, the standard birthday celebration at dinner is as above.
If everyone wants to eat cake, it is "free" (included with cruise fare) as long as it is served by the piece. You only have to pay to get a full cake which they will then cut for you. Honestly, that's a waste IMHO.
If you are meeting up with the family a day or two before the cruise or hanging out with them a day afterward, buy a cake in Florida and do the cake bit in the hotel or wherever. Do the standard birthday celebration on the cruise.
And a note--the cake on the ship isn't all that good. Seriously, standard grocery store bakery cake is better than some of the ship cakes. Their other desserts are good, but the cake isn't. In fact, my daughter learned as a kid that the nicer it looked, the worse it tasted. The "plain" ones tend to be better!