I recently went on a Disney Cruise with a 3 year old and a 17 month old. We wouldn't have chosen to go with such young kids (especially the 17 mo old), but we too joined our greater family for vacation. Disney, of course, was unique, because it was geared for kids. But that being said, it was not ideal being there with a 17 month old. They did allow us 10 hours of babysitting for him but on a 7 day cruise, that wasn't enough!!! We did find it a challenge not allowing him in the pools, particularly because the little splash pool he was allowed in only had 2 inches of water in it and it was right next to the kids pool. As you can imagine, he was not happy with his own situation and wanted to be where the other kids were.
Even with the limitations, I will say that we had a great time as a family. We took full advantage of the ports of call. We were in the Caribbean so we got off the boat and found the nearest beaches to play on. Because it was Disney we were able to take advantage of on board activities geared towards kids during the day. But of course he was really too young for a lot of those. We enjoyed a lot of relaxing time just sitting on the top deck enjoying the warmth and letting him walk around and look out over the ocean, which he loved. My husband and I also took turns watching at different times each day, one letting the other go have some adult time. Also, our extended family was great about watching our kids a few times on the trip so that my husband and I could spend some quality adult time together. We also took turns at night staying in the cabin with the sleeping kids so that one of us could go to the shows. I know that a lot of people put their kids down in their cabins and then went out. I wasn't comfortable with that.
Anyway, you can have fun on the cruise even with the limitations of being with little ones. After all, I figured that being on a cruise with little ones was better than not being on a cruise at all!
I would look into whether there are any options at all for babysitting and if there are, take full advantage of it. Otherwise, make plans with your spouse and, if they are willing, your family to share in some of the babysitting duties and give you a few breaks over the course of the trip. The little ones will find the experience of the boat fascinating and will just love being with the family.
Good luck and have a great time!