I'm not sure what the OP is asking for either. Periods shouldn't hinder your time at Disney. You should be able to do everything you want to, even swim, with the right supplies. Medication that will ease muscle spasms, nausea, and pain can be an asset if that's an issue, and I would speak with your doctor ASAP if that isn't being managed already. Otherwise, there are plenty of toilets in every park, marked on every map, and Cast Members will always know the nearest one. Be sure to make frequent toilet breaks and change your supplies more often than you would at home, as Disney queues and other distractions have a tendency to delay planned toilet breaks.
I also echo to bring more supplies than you think you will need, and carry extras with you each day. Bring an extra pair of panties and shorts (and a zip top bag) if you're really concerned about leaks. The parks and resort hotel DO have feminine supplies and pain medication, often behind the counter if you ask for them. They can be tricky to find, but don't be embarrassed to ask, or go to the first aid centre if you need to. I can reassure you that you wouldn't be the first person to ask for such supplies - we've had to ask for anti-nausea and pain medication before, too.
This is coming from an athlete with painful and heavy periods and ends up ghostly pale and writhing in pain without appropriate medication. My doctor worked with me to manage my periods so they rarely interrupt my training or life any more (without the use of hormonal birth control). On a month's notice (or less), you may not get complete control of your symptoms, but your doctor (or pharmacist) may have some great suggestions to make your vacation more pleasant.
Medications your doctor or pharmacist may suggest: Midol, Ibuprofen, Acetaminophen, Meclizine, Compazine
Best of luck! Have a wonderful vacation.