Stop worrying. Diabetics go to WDW every day and do fine. Carry some quick sugar just in case. Should do that anyway even if you aren't in Disney,
As to refrigerating the insulin, it is not necessary. The vials in use can be left on the bedside table for a month without refrigeration. Do it all the time. The rooms are cool enough that there is no problem. If she uses Humalog then use a cooler pack. But N, R, L, SL, ect do not need refrigeration except before you open the vial.
If she is carrying it to the parks then she will need a small cooler pack to keep it cool. FRIO makes a nice one that works on evaporation. You ca find their site on the internet.