The lawyer in Florida would either have to 1) be a member of the California State Bar (you don't have to live in California to be a member of the California Bar) or 2) petition the court to appear pro hac vice, which means a California lawyer would agree to be your attorney of record, but the Florida lawyer could appear for you in court.
Keep in mind that a family law case can take many, many court appearances, and you would probably have to pay the Florida lawyer's travel expenses for each of them.
It is true that a family law matter requires many appearances but that doesn't mean the FL lawyer would fly here for all of them. More likely the CA lawyer would do the routine appearances in consultation with the FL lawyer who would fly here for important contested hearings.
Even so, I can't think of a worse situation than having your primary lawyer on the East Coast. It is also true that FL is not a community property state so that lawyer may have to spend considerable amounts of time educating himself to CA law and procedure. It won't cost double what a CA lawyer would cost; it'll end up being 4 or 5 times as expensive.