You could always bury a cache of supplies. Just be sure the container or contents are watertight. As a FL guy, no stranger to hurricanes. Does your trailer park have any kind of cement block structure? (like a rec center, or office, etc.?) If so, then this would be the logical quick place to go for a tornado. Of course, as in FL, you aren't likely to see any tornadoes above an F2, so your safest bet would be in a bath tub, with a mattress over you (if you don't have time to get to a better structure). Wandering outside is no place to be in a tornado, even a minor one. Just one blown board could be deadly. I know, I've driven through an area with an active tornado before (had to get my brother out of there). Looking back, it was a really dumb thing to do. He was fine where he was. I ended up with damage to my car, but I still feel lucky.
For hurricanes, have a Go Bag that contains the essentials, and bury a cache of other supplies (to be retrieved later, when you CAN carry them off). Again though, having SOMEWHERE to go is of primary importance here. High ground, sound structure, and hopefully friends with a like mindset of prepping would all be best. Even in minor hurricanes, trailer parks are MANDATORY evacuation areas, so you should also check with your family (are they going to a shelter? are they going to a relative's?)
In most cases, you've have at least a day or two notice of an impending hurricane, so this may give you a chance to prep a bit more at whatever location you're going to.
Some basic rules (as a hurricane approaches). (this is my own list, not some canned one)
1. Fill up the car with gas (as much as you can), as gas station pumps may lose power, and be out of order.
2. Get a good deal of cash out of the ATM (same reason as above, power outage means no ATM).
3. Have a weapon (even if just a good knife). Being armed makes less chance of being a victim.
4. Secure any loose articles around your home.
5. Tape or board up your windows.
6. Have a large tarp or two (in case of a roof breach).
7. More for your parents, be sure they have any paperwork they need with them.
8. Take pictures of expensive belongings (for insurance purposes, if they have insurance).
9. Make sure any family photos are in a safe, waterproof container.
10. Take any steps you can if you have pets, to keep them safe.
11. Have some kind of non-electric means to cook food (like a camping stove, or a portable grill).
12. Make sure you have flashlights, LED lanterns, etc. and batteries for them.
13. Make sure you have a radio (for news).
14. Fill tubs, sinks with water (for washing, should have bottled water for drinking).
15. Get bags of ice. Put them in your fridge and freezers (will help keep items cool if power goes).
16. Trim back any branches that are close to the home.
This is all in addition to having other items like spare food, water, medicine, and other preps. The above is really more what you do in those 1 or 2 days prior to the storm arriving. (and I'm sure I'm forgetting a few)
