No, your daughter's father will not be able to add her to his car insurance policy in New York since she lives out-of-state in Florida.
If she comes up to visit him, his current car insurance policy should cover her while she drives his cars in New York, without even being added to it. It will not however extend to her driving her own car or other cars in the state of Florida.
Your daughter doesn't live in her father's household and that is why his automobile insurance company would not allow him to add her to his policy. Also because she is in Florida and not New York, she has different car insurance coverage requirements and thus needs to get a Florida car insurance policy.
If she plans to get a car then she will need to get her own auto insurance policy, since you do not drive and thus do not have a policy to add her onto. Since she is newly licensed her rates will be high, she will need to shop around to get affordable car insurance.
If she doesn't have a vehicle of her own yet, but you want her to have auto insurance coverage anyway, then she can get a non-owner's policy.
Non-owners insurance gives Liability protection for when a driver is at-fault in an accident, but they do not own a vehicle. Non-owners policies typically will include Liability coverages of Bodily Injury and Property Damage, Medical Payments, and Uninsured/Underinsured Motorist coverages.
A non-owner's policy is secondary to the actual car owner's insurance. This means if your daughter borrowed a friend's car, then the car insurance coverages of that friend would be primary if your daughter was in an accident. Your daughter's non-owner's policy would only be used if the car owner's Liability limits were exceeded and her insurance was needed as secondary or excess insurance.
When obtaining a non-owner's insurance quote, on the vehicle screen mark the option where it says "Check this box if you do not own a vehicle and would like to purchase a non-owners policy" then proceed on with the quote.
If your daughter has a car, then she will need a full personal auto insurance policy for that vehicle. Your daughter can get started on a quote for a non-owner's or regular personal auto insurance policy by clicking here for online car insurance quotes with CarInsurance.com.