I think you have enough on your plate. As you know I take care of my elderly friend. There is a lot to it way beyond the finances. Do you really want to take on the stress? I get calls at 5 am saying my little old lady is on her way to the hospital, can I please meet her there, or she has fallen, can I come up right away. And she's in good shape! Yesterday the call was that the insurance company didn't pay for her meds, so the meds she needs on Friday, won't be delivered. 14 phone calls later, her meds will be on the way in the morning. Now I'm up working at 12 o'clock because I spent the day dealing with this..and it can't be pushed aside. It has to be done when it has to be done.
While this is your mom, and you would want to be with her..dealing by yourself IMO isn't a good idea. I've had a dad with Alziemers, and it was hard. When she is confused and very agitated, you may be called. It's amazing all the times the nursing homes call. Especially in our area, since so many have had serious problems, and they want to cover themselves. I think you really ought to think about this very thoroughly. Since you will be spending a good part of the winter in Florida (and if you are her caretaker, would you be able to even leave? Your daughter has a lot on her plate too, so it would be hard for her to stand in for you for months), I would strongly suggest you guys move your mom to Florida. In her shape, she prob won't realize it, once it's over, and your two siblings are there and you will be for part of the year..and you can visit other times.
Please don't offer to take this on right away. Think long and hard about it. You have had so much going on..you don't want to end up in the room next door to her.
By the way..as someone said in another post, my dad was the same way. Each time he found out my mom was gone, he grieved hard, all over again.