First to answer the question "What to do with my elderly father? " - Love him. Okay, had to get that out of the way. :)
Have you sat down and talked to him about your concerns? Has he had a recent medical checkup? As we get older our reflexes slow down, along with vision and hearing acuity. So this may just all be a result of a natural organic process - BUT only a physician will be able to tell. Ask you father, since he is now living in a different state, to have a complete medical workup so that there are current, up-to-date medical records available. With HIPPA laws the Doctor may not be able to release a lot of medical info to you but if you explain, before the appointment, that you need your father cleared for driving, he should be able to give you a heads up one way or the other.
See if there is a defensive driving class in your area for seniors. Try and get a copy of the accident reports to see what the situation was at the time of the accident and ascertain if that had any bearing on the accident occurring.
If you father is driving 19 hours to FL regularly, I think it indicates that he really doesn't want to live in Ohio. Is there anyway that he can remain in FL? It is very hard to relocate at that age and realize that you are losing your independence, and your friends and community. Yes, you will worry about him aging and being so far away from you - but I learned when I moved my Grandmother to me that taking her away from her community "aged" her faster. It was very hard for her the first year or so.
As for forgetting things - again that is an organic process - and let's face it we all have forgetfulness. Also, he could be experiencing "selective" memory and just ignoring the things he doesn't deem important.
Bottom line is you need to find a way to ensure his safety that leaves him his dignity and independence for as long as possible. It is really hard when are parents age.
Good Luck