I was a teen in the Tampa Bay area and did all my commuting to school by bicycle. With fenders and a raincoat you should stay generally dry. You don't say how long your commute is, which is a major consideration. Orlando is generally pretty flat so you don't need major bicycling firepower. Three speeds are all you need really. And unless you have extreme distances, a used bike properly chosen, will deliver what you need for far less than $800.00. My current ride is a mountain bike streetified with slick tires, fenders, lights, a rack and it ran me about $100.00 total when I first got it and accessorized it. (Yeah the bike was a FREEBIE!) Admittedly, after 5 years of hard service I did put it in for an overhaul and spent 300 on that. LOL.
Basically you are washable. Unlike the Wicked Witch of the West, you won't melt. If you just put dry clothes in a sealed plastic bag and get wet, you'll still get where you are going. The rain in Florida tends to be warmer, so choosing to just get wet is a doable option. And I noticed that when I lived there, it may rain frequently, but it doesn't rain all day. I used to time my recreational rides in summer. Ride west in the morning, turn back east when I saw clouds and arrive home just before the rain. You will often be able to time your ride to avoid the rain. Modern weather services such as weather.gov make doing this much easier.
And yes, your father is trying to do what is best for you... as he sees it. At times, my father opposed my bicycle commuting which I didn't understand since he had bicycle commuted himself. Turned out that stopped when he got hit by a car pulling out of a driveway. He even urged me to ride a motorcycle instead. Though that sentiment disappeared when my step-brother got left-hooked by a schoolbus on his motorcycle.
So yes, the streets out there are tough. I attribute my current fearlessness in traffic to my days in Sarasota, St. Pete and Tampa. Take care to learn the ways of traffic. The League of American Bicyclists offer courses in
Traffic Skills 101, Traffic Skills 201, and Commuting. Taking classes like these may go a long way towards convincing your parents that you will be safe and that you are committed to doing it right.
Good luck.