I want to make mom happy, should I go on small vacations or really want to move to Florida?

Still not much info. Moving, I wouldn't suggest it. Taking a Dementia patient out of familar surroundins causes anxiety problems. Short trips too. If you can find someone to care for her while you take a short trip that is good. Gives u a break. Medicaid would be another thing if you feel u may need it. You move you may have to have residency for a yearvor more before she qualifies for any services. Mom could get there and the say she wants to go home.

I live with her since 2015 and I am the caretaker.

Could you give a bit more detail? It's not clear what you're asking. Where do you live now, and where does your mom live? Is your plan to move away from her or bring her with you? Is there someone to take care of her if you move away, or is she in a facility?