Welcome aboard, Laura!
Disney Cruise Line is happy to seat groups together if you link your reservations and make a request for that. However, normally, they will only seat up to eight guests together. I do know that with special requests they have been able to sometimes seat up to 12 together. With 13, you may need to be at two tables. I'd advise you to get the reservation numbers of each party in your group and call the agents at Disney Cruise Line at 800-951-3532 to discuss your options. You may be able to have two tables next to each other, and with the same service team, so that you can switch up who sits where each time you dine. No need to arrive early to get tables, as your table will already be reserved for you each night. I mention the service team because you'll have the same servers every night for dinner, as they meet you at the next restaurant in your rotation each night. This is all part of Disney Cruise Line's
Rotational Dining. It's so nice as you get to know them and they get to know your preferences. Each time we've sailed, our servers have become like part of our family, telling the kids jokes, doing magic tricks for us, and simply having fun chatting with us. There are always a few tears as we say goodbye to them that last day. I know you'll find that your servers are simply magical as well, Laura!
As far as dining times, we love late dining so we're not rushed after our days in port. If anyone is hungry, I assure you snacks are available throughout the ship before dinner! You'll enjoy more time to relax after a day in port, shower, get dressed an enjoy the nightly show before you eat. Plus, the toddler can take a late afternoon nap and not be rushed to wake up to get to early dinner!
Have fun planning your cruise and stop back if you have any other questions before you set sail!