Actually you can do whatever you want. It's only going to matter if you get pulled over or one of those 2 states decide they want to look into it.
Now about getting pulled over, the police might wonder why you have a different license that what the MH is registered, but then that also depends on where the insurance is held for the MH.
I could ASSUME that since the MH is registered in FL. the insurance is also for FL. in order to meet the minimum requirements for the state that it is registered in???
As I stated it only matters if you have an incident or get stopped.