Welcome aboard, Matthew! The Western Caribbean itinerary is one of my favorites with Disney Cruise Line, so I just know you'll enjoy choosing from the amazing Port Adventures that Disney offers in each of its ports of call.
My family and I are Catholics too, and take our Sunday Mass obligation very seriously. Unfortunately, there is not normally a Catholic priest onboard to offer Mass each cruise. There is a priest onboard over Christmas and Easter, which is wonderful because Catholics onboard can all celebrate these holy days together in the Mass, and daily Masses throughout the sailing as well! But, since you're not sailing over one of those holidays, most likely a priest will not be onboard. There are sometimes non-denominational
religious services onboard, but I know that doesn't take the place of Mass. When we sail, we look up the Mass times for local Catholic churches in the port of call that we are visiting on Sunday, or Saturday late afternoon if the ship is in port late. If you don't know about it already, check out Masstimes.org, a great website which will tell you the location and Mass times all over the world! We use it every time we travel, and enjoy participating in the Mass in different cultures!
I noticed, though, that your family will be at sea on the Sunday of your itinerary, and you're boarding the ship Saturday afternoon. That means that you will not have access to Mass that weekend, since no Sunday Mass is available, which means there is no obligation, as it's not your choice to not attend since there isn't a Mass at sea. You may consider spending some time in prayer that morning with your family, perhaps reading the Liturgy of the Word for that Sunday. Chat with your parish priest if you're concerned about this, Matthew.
Please stop back if you have other questions before you head out for your exciting Disney Cruise Line adventure!
Marcy