It would probably be helpful for the ill brother to resign and then you can replace him. I would hire counsel in FL to advise you. The trust document will tell you what happens and what to do.
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The law of the jurisdiction in which the Trustor is located will govern. Sounds like that is Florida. But, the terms of the trust will typically prevail unless prohibited by law. So, the trust, and all amendments to it, need to be reviewed. You may or may not need an attorney in Florida, but hopefully the trust was drafted by an attorney there. If so, he or she may assist. If you wish to consult with a Tucson attorney to review the trust and advise you further, I am available to see you next week. Just call my office or email me to schedule.
The above "answer" is for discussion purposes only and is neither intended as legal advice nor to create an attorney-client relationship. An attorney-client relationship is not created until after an in person consultation and I agree in writing to provide representation. I am licensed solely in the state of Arizona. You should consult with a knowledgeable attorney in your jurisdiction.