On our second cruise we put DD in the nursery one night. She was 22 months at the time was only ever home with Grandma during the day when we were at work and never had a babysitter. We we so worried but she literally ran in there and didn't look back. She wouldn't ever let us hug her because there were too many fun things. It's not like dropping your child off at daycare or school because there are Disney Characters in there! And tons of fun things to do. As mentioned check out the open house the first day. Hopefully there will be less separation anxiety and the CMs are amazing in there! DD starting going to the club alone when she was three (we didn't sail with friends) and I had this image of her being trampled by 12 year olds while she wandered aimlessly. Each time we picked her up she was with a group of girls her age and a CM leading an age appropriate activity.
Be also very clear with the CMs that you don't mind being called. They are so used to parents who say don't call me because my kid has been crying for ten minutes and get annoyed when they call. We always tell DD that if she wants to be picked up, even after 5 minutes, to tell the CM and we'll pick her up. This made her feel more comfortable going since it's not like when she's in preschool and we leave her for 9 hours.