Car seat, car seat, car seat for the younger one. A toddler will be wiggly and squirmy on your lap and if the flight is of any duration beyond, oh, 10 minutes, you'll be exhausted and sweaty and frustrated from handling a struggling 18-month-old on your lap. Besides, if we'd put our children in a car seat in a car, why wouldn't we want our children just as well secured on an airplane? Turbulence has thrown adults around; imagine what it could do to a small child. It's more expensive, yes, but we've flown many, many times with our daughter since she was 5 months old and always get her her own seat.
If you do have to go with the toddler on you lap, go online and find a reputable "seat belt extender" specifically for use on planes. Or the airline may have these, but check well before you get to the airport; with airline cutbacks these days, don't depend on the airline to provide these. These belts help hold the baby on your lap. But again, for safety and your own sanity, I'd buy the toddler a seat.
Be sure your car seat will fit the airline seat. Car seats will claim they fit "standard" airline seats but I hear it isn't always true. Call the airline well in advance to check. Some airlines do have lists of seat brands they know for sure fit their seat, or they can give you dimensions of seats that will fit.
Take the kids for a LOT of walking in the terminal prior to the flight and then for a stroll up and down the airplane aisle, if possible with the carts of food etc. going around, during the flight. Have distractions -- we always bring something that our child has never seen before; a new toy, book, etc., or several new ones for a child as young as the 18-month-old, since the attention span is shorter.
Regarding renting cribs: Again, over the years we have had friends with nightmare stories of rental cribs that were in poor condition, and you have no way to know if your rental crib is one of the many recalled ones from recent years. Rental cribs often are old, and may or may not come with sheets, which may or may not be up to your standards of cleanliness. I'd take the pack and play, newer and safer and you don't have to wonder about it.
I just heard from a friend who was delayed overnight getting somewhere last week, and didn't have any luggage, since it went on another flight. So assume that that could happen and be sure you have a carry-on with essentials if you absolutely had to spend an unexpected night in a hotel with none of your luggage!
It's not all that intimidating, really...Have fun in Florida and know that the travel part is only temporary!