OK. I would say go on the vacation if the kids are well enough to fly. You could use some Florida sunshine. The days are usually warm right now, but the nights are cold, so you will need some warm clothing. Take it easy on the vacation. Don't do the parks from 10 AM-10 PM. Take it slow. Just get out in the sun and try to get better.
As for the relationship. Well, you need to go to counseling and try to work things out so you understand each other better. This is too painful to continue as is. But the kids deserve better than parents who just throw away the family.
So try to get him to agree to just that. Nothing more. Retrouvaille could work, or once a week counseling.