Ahoy there Taryn,
You must be so excited about setting sail around the Mediterranean onboard the beautiful Disney Magic!
My family experienced this Cruise last May and I can tell you that you are in for a real treat.
Children are absolutely allowed to remain onboard the Ship whilst you explore the fabulous Ports of Call and my Son chose to do just this when we visited Ajaccio, Corsica. Just be sure to let the Counselors know that you will be leaving the Ship when you drop your twins off at their choice of Youth Club.
You will also be pleased to hear that children are invited to enjoy lunch and dinner at the Youth Clubs so, there's no need to worry about them going hungry whilst you are enjoying some wonderful European cuisine.
I have no doubt that your 5-year-old twins will have a blast at both
Disney's Oceaneer Club and
Disney's Oceaneer Lab. My then 7-year-old Son enjoyed it so much we had difficulty at times getting him out of there.
Wishing you a magical holiday! Bon Voyage!