First - See if it actually requires refrigeration or if refrigeration is preferred.
Many liquid antibiotics don't actually need refrigeration - they just need to be kept cool, not cold (i.e. room temperature, not over 80 degrees).
Some need refrigeration, but only if you are storing them for a longer time period than your child is likely to be taking it.
Many say refrigeration is preferred, but the medication can be stored at room temperature.
In some cases, it is refrigerated because it tastes better cold and the child is more likely to take it. If that is the case, you can hold it at room temperature and just cool the dose before giving by placing it into a ziplock bag inside another bag with ice.
Check with the Pharmacist (someone who will actually look up the medication if they are not sure, not just say yes it does). The Pharmacist would be a better choice for that information than someone at your doctor's office.
Second - They do have medication refrigerators available at the resorts. Just explain you have a medication that needs refrigeration. The refrigerator they give you may be tiny (the size of a shoe box). Even if it's a bigger dorm sized one, it's important to not freeze your medication. Sometimes the refrigerator is set on the highest setting to get it cold sooner. Things put into it can freeze easily if you are not careful.
Third - If it does need refrigeration, you could do what your DH suggested. You should have an ice bucket and can get ice easily. Bring a zip lock bag to keep the medication bottle from getting wet. You also don't want the bottle sitting directly on the ice - to keep it from freezing.
For park days - Medications can be stored in First Aid in any park. The location of First Aid is marked on the park maps and they are mostly right next to the Baby Care Centers.
Tell the CM that you have a medication that needs refrigeration. They will have you fill out a form and then safely store your medication for you until you need it.
If the medication dose just needs to be cold for better taste, you can cool one dose like I mentioned above. Ice is available free of charge from First Aid or from any of the counter service restaurants.
PS - If you are traveling by air and the medication does need refrigeration, you can bring a gel pack or something to keep it cool. Just make sure to have that and the medication separate as you go thru security and show them to the TSA people. You also could bring a small cooler with ice, discard the ice before going thru security and get more ice when you get to the other side. Some people have also frozen small bottles of juice (3 ounces or less and put in the bag with your liquid items to go thru security) and used those to keep the medication cool.
You would have to show TSA an ice pack, but if you don't use one of those, just put the medication with your other liquids in the one quart bag to go thru security.
