If my 21 year old daughter has an accident/ or other infractions in a car titled in my name, can I be liable for the damage or incident?

In Florida, the owner of a car is just as liable for injuries or damage that the negligent driver causes as the driver is. Florida is a state where cars are considered a "dangerous instrumentality" and an owner of a car is liable just for owning the car. Since your daughter is 21, there is no legal need to have your name on the title, so you might want to consider putting the title to that car in her name only.