If the dog has been trained to detect low blood sugar and alert your dad in some way so he can do something about the low blood sugar, then he can legally it is a service dog and he can bring his service dog with him as an accommodation to his disability.
There is no requirement under the ADA that a service dog have a vest or ID card identifying it as a Service Dog.
Most Service Dogs do wear a vest or other visible sign for 2 reasons:
- it lets other people know the dog is working, so they (hopefully) leave it alone.
- it is a 'uniform' for the dog that tells him/her that they are working and need to behave in an ' on the job' sort of way.
If your dad wants something to show because it would make him feel more confident, the person who trained the dog for him should be able to provide something.
He should be prepared that he can be asked if his dog is a service dog and what the nature of the service the dog provides for him is.
The other question is whether or not the dog is prepared for what he will experience when he is out, especially if he was not professionally trained.
A pool is a very noisy environment, with lots of splashing and movement.
A theme park is sort of total sensory overload for a dog - lots of smells, unusual sounds, movement and commotion.
Plan that if the dog does come, he will become tired more quickly than at home and will need breaks in places that are less stimulating.
Since your dad lives in Florida, the heat and sun might not be a problem - unless the dog is mostly used to being inside in air conditionditioning.