Birth certificate is just so they know the child is under 2. They may or may not ask for it. If you are not leaving the country, the permission from the non-traveling parent isn’t an issue.
I have done 4 flights to and from Orlando alone with my 2. Their dad is deceased. No one ever asks about him. The guy at security would just ask my older child who she is traveling with; but that would not apply in your case.
When my son was near 2, the guy at security in Orlando did look at his boarding pass and call his name to see if he responded. My son looked at the guy when he heard his name and we went on. That’s the most that has ever happened at that age.
Flights to Orlando tend to be full so I would not hold out much hope on an empty seat. I would ask upon your arrival at the gate if the flight is full and if need be go ahead and do the gate check process for the seat at that point instead of waiting for boarding.
One note: you didn’t mention if your flight stops anywhere on the way to Orlando. If it does, see if they can tell you if the flight will fill at the next stop because if you by chance do get an empty seat and the flight makes a stop and more people get on, you might have an issue and have to give up the seat.
That being said, have a nice bag for the seat if you don’t have one already. If it is a large seat, be prepared for them to hand search the bag if it won’t fit on the belt at security. I had that happen once. If you do end up taking it on the plane and using it, they have to be installed in the window seat.
If the child likes fruit snacks or another gummy type snack, those are helpful for ear pressure. The back of the plane is the place to be.
Unless it is a really long flight, don’t feel the need to pack everything he or she might want to play with. I did that and my son spent most of the flight playing with an orange I had gotten before we got on the plane. My daughter at that age was more interested in snacking and looking out the window. Still is actually.
I hope it goes well for you. My daughter was a dream when she flew as a lap child. My son was totally different so he never did although he would spend time in my lap once the seat belt sign was off.