I can understand why you're really torn, but can't help you make the decision.
As others have mentioned, the second dose of the Covid vax can pack a big punch. While DH and I haven't yet received it, our daughter (age 25, currently on emergency medicine rotations) received the second dose and had several of the typical reactions. My MIL (age 90's) received the second dose and had no reactions, whatsoever. Go figure.
Also, keep in mind that it typically takes a few weeks for the body to build immunity after vaccination.
I don't think anyone mentioned this, but if you go to FL, what's your state's re-entry procedure?
In NY, travelers must obtain a test within three days of FL departure, prior to arrival in NY. The traveler must, upon arrival in NY, quarantine for three days. On day 4 of their quarantine, the traveler must obtain another COVID test... If both tests are negative, you are free

! This essentially turns the 10 day quarantine into a +/- 6 day quarantine. This is still the rule in NY, even if the traveler has received both shots.
Are you and your wife both OK with you coming back to your home after traveling, or will you need to find somewhere else to isolate, as you await the results of your Covid tests or wait to make sure you don't develop Covid (unlikely, because you'll be vaccinated)?
All the best to you, whatever you decide