I totally understand about needing the lap pool for swimming. My 16 y/o daughter was a competitive swimmer for years. We finally had to let it go a couple of years ago, due to school sports and cheerleading. We also took our first Disney vacation since she was about 5 years old once she let go of the sport.
I know how important it is to continue the workouts, and I agree with checking into the YMCA pool as well. I know there are teams in the Orlando area. Have you tried to contact any of them to see if the coaches would mind letting your children do the workouts with their teams? I would let them know they will be in tapering mode at that time also. Are they preparing for a really important meet? If so, I would try to schedule your trip for a different date, or make sure they train with a coach on one of the teams there in Orlando. I have done this for my daughter while visiting family in Alabama. Once they are USS registered they should be welcome at any pool with a competitive team.
I forgot to say "good luck" to your children for whatever meet they are training for. Swimming is such a good sport, and I have found myself missing the meets and people I have met during all of our travels. My daughter has decided to give up soccer this year, and wants to get back in the pool. She lifeguards here in town, so she keeps up with lap swimming. Swimming is really her great love, but we live one hour away from an indoor pool for training.