IIRC, the law governing the estate is not that of the state in which the will was drafted, but the state of residence. So unless your mother resided in FL, the law of her state controls.
You may or may not need or want to get a lawyer. I am in the final stages of administering my mom's estate (administration being what one does with an estate where there's no will, as opposed to execution of an estate under a will). I am a lawyer, but not an estates or probate lawyer, so I was as uninformed about California law on the subject as any other lay person. (And, yes, I know the one about how a lawyer who represents himself has a fool for a client!

) I got some help from my colleagues who are probate lawyers, but one of the best resources was simply the state probate code. So you could represent yourself, but whether that is wise depends on a few things -- are you good at coming up to speed on what can be relatively complex issues on your own? Is the estate and its bookkeeping relatively simple? Will estate taxes need to be paid? Will the will be contested by anyone? Are there a lot of creditors to the estate (bills your mom had owing when she died)? In retrospect, I might have hired a probate lawyer, since figuring it all out plus the emotional burden was rather difficult. In any event, some lawyers may give you a consultation without charge, and you should call around to various probate lawyers to see who will. Although, bear in mind, they are not going to give you much (if any) advice, but merely evaluate the case to see whether it is worth their while to take the case and what it might cost, usually.
At least in California, I've learned, an estate with a will does have to go through probate. Generally, only assets that will transfer automatically on death, like accounts with named beneficiaries or jointly-held property, are exempt from probate.
There may be some deadlines that you don't want to miss in the first year after your mother's death, so the sooner you start working on the estate, the better. Regardless whether you consult a lawyer on this, you should begin to educate yourself on the law and the procedures. Probably there are some basic "Dummies" kind of books on probate for your mother's state. For example Nolo Press provides a good bit of material on
California probate (and that link probably has some info that is worthwhile in many states). Your local bookstore may be able to help, or Amazon/BN, or findlaw.com, and even the website of the probate court in your state (or your mother's state, if different) may have links to info or an info line if you are representing yourself (
in pro se or
in pro per).
I don't understand what you mean by your father insisting that there is something else you have to do. Does he mean something else other than execute the will?
I hope this is somewhat helpful. It should be clear that none of the above is legal advice, BTW!
I'm sorry to hear of your losing your mother. It was a very difficult event and change for me, and I am sure that it is for you, too. Having to monkey about with the estate adds stress to the whole crappy time... Feel free to e-mail through my profile on MacNN me if you can't find sufficient resources through the above sources.