If you Will was valid in Maryland it would be valid in Florida. However, every states laws are very different and I would suggest that you consult with an Attorney in FL related to updating your prior Will.
Letters of Administration will need to be certified within sixty days for a bank to honor the document. You also would still need to be actively serving as Personal Representative and not have been discharged through the Court. You can request updated certified documents from your Attorney or the clerk of court.
Typically someone needs to be related by blood if they are located out of the state of Florida, however there are some exceptions that would allow certain non-blood relatives to serve. If your intention is to have a law firm serve as your Personal Representative, we would be happy to discuss what would be involved. Remember you can always change your Will and change who you have serving as Personal Representative.
Assets that were jointly held with another person upon death would become the property of the surviving person. The will is not invalid related to any other assets that were not jointly held. You should consult an Attorney if you feel there are other assets that were not jointly held or if you believe some type of undue influence was involved related to the transfer of any of the decedents assets prior to their death.
It would appear from your Question that the Attorney is trying to substitute an informal accounting for a formal accounting. A formal accounting can take more time to prepare, however you are entitled to the same as a beneficiary and should hire an Attorney of your own if you feel your rights are not being represented. It should not delay an estate to prepare the accountant. You can also try to contact the Attorney for the Estate directly and see if they can help clarify what is happening in...
I am very sorry for your loss. If there was a Will, it should be filed within ten days of death. You will be able to view the Will at the Clerks Website for the county in which your mother passed away.