Ahoy, Jennifer!
Thank you for sending in your question to the Disney Parks Moms Panel. Sometimes the logistics of getting to and from the port with carseats can be tricky! I have a couple of suggestions, but please feel free to reach back out if you need further help.
Since you are planning to visit New York prior to your cruise, you may want to consider staying at the New York Marriott Marquis in Times Square since Disney Cruise Line offers an option to purchase
ground transportation from this hotel to the Manhattan Cruise Terminal. If this hotel doesn't work for your entire stay, maybe consider staying there the night before you set sail. You can also purchase a transportation voucher through Disney Cruise Line from the Port of San Juan to the airport for your return. You can add transfers to your reservation by calling (800) 951-3532 up to three days prior to your departure.
Another option is to look into a car or shuttle service. Many offer SUV or vans that would allow you plenty of room for the three car seats. I've utilized a car service in both cities and found them very convenient, so I think this is another good option for your crew. If this is the route you plan to take, I recommend doing a Google search and then reaching out by phone or email to inquire about using your own car seats in the vehicles.
Jennifer, you are going to love cruising out of the Big Apple! The views from the deck are just spectacular. Have your camera charged and ready to capture the gorgeous skyline, sailing right under the Verrazano Bridge and your sailors waving bon voyage to Lady Liberty. It's one of my favorite ports to experience a sail away!
Thanks again for sailing by the Disney Parks Moms Panel! Please don't hesitate to reach back out with additional questions. We are always happy to help.
Nancy