Just wanted to say you are not crazy for doing this. We have cruised with all our kids, starting from when the youngest was 8 months old on a Transatlantic. We've since done Caribbean, Panama Canal, Alaska, and Baltics - all with at least one baby/toddler and at most three. Hardest one was definitely Alaska on Celebrity as they had absolutely nothing for those under three. Still, even that was a great week!
No it will not be as relaxing as it would without children, but it's still fantastic plus someone else has to cook and clean. Saying everyone will be miserable is just plain wrong (not to say there won'tbe difficult moments but you get those at home with kids too). Pep talk concluded, you have a great holiday! We had actually booked this one for late October with our 4 kids aged from one to ten, but then changed to ncl breakaway out of NYC instead.