well what I am going to tell you is my opinion as a father.
In order to understand my opinion I can tell you this I live in Puerto Rico and I already took this cruise 3 times already and I took the same route you will have on april on the carnival victory during this past summer.
NO DON'T TAKE YOUR KIDS WITH YOU,
this an active cruise 7 islands on 7 days they will not enjoy a cruise like this one
well here are a few reasons:
1. As I remember kids at that age don't tell you how they feel if they are sea sick they will keep suffering and you will not know what's going one and remember that if you use their medical service at the ship the price $$$ is really high. Besides the caribbean weather is not something your kids will enjoy if they get bitten by a mosquito or something kids can get really sick and really fast at that age.
2. If they don't have sea legs, even a lot of adults don't have them, they will get sea sick on the third day of your cruise when you will be on route to Barbados and on the 4th day. I tell you this, on my last cruise on carnival victory I saw a little kid around 2 years old on the same situation even the waiter told me
"I have been on this route a few months now and I can't understand why they bring kids at that little age they are just going to suffer in this trip with this sea"
3. Think about the people on the cabin next door
,I got kids don't get me wrong, but I don't take them on a cruise until they are ready to enjoy it, also a baby crying during nights is something only a father understand but if the people on the next cabin want to sleep they don't have to, they will just call Guest relations and the system will do the work.
my advice leave them with some responsable adult at home if you can and go to the cruise but use the time to enjoy it with your wife...