This is highly dependent on a number of issues so this question can't really be answered without referring to state law and the situation. As a very general rule it takes 2 - meaning if there is some question, most powers of attorney state that it takes the agreement of 2 physicians to certify that someone is incompetent. However, in many situations one is enough. It probably could not hurt to have a second opinion.
With respect to your question "Does this preclude other family members from trying to alter her will," I do not know what that means. If she is incompetent, she cannot then change her own will. If she attempts to make a change after being deemed incompetent, it could certainly open the door for family members to challenge the will.
This is not legal advice nor intended to create an attorney-client relationship.
Q: Is one doctor's diagnosis and letter sufficient to declare her incompetent?
A1: If you're in probate court trying to get guardianship/conservatorship, if depends on whether the judge accepts your expert witness.
A2: If you're trying to "activate" a Power of Attorney or trust succession plan, it depends on what the document says is sufficient.
Q: Does this preclude other family members from trying to alter her will, or do I need more physicians to certify her incompetent?
A1: They can try all they want, but the current findings would be good evidence that she lacked mental capacity at the time of alteration.
A2: According to Mae West, "Too much of a good thing is... wonderful!" and maybe the same can be said about evidence; generally, the more the merrier, but I think you're on pretty solid ground (again, depending on what the documents actually say).
The short answer is that it depends on state law, as each state is slightly different.
In Colorado, no doctor has that power, as only a Court with jurisdiction can declare someone legally incompetent (the Court will usually rely on one or two doctor evaluations as part of the process). However, many legal documents, such as trusts or powers of attorney, are drafted to allow for either one or two doctors to certify in writing that someone is incapacitated in order to trigger the documents. It will also depend on what you are trying to do, as different entities require different levels of proof.
This does not preclude her from changing her Will, as the capacity to create a Will is generally pretty easy to meet, and you only have to have capacity on the day you change your Will. Some people move in and out of capacity depending on their condition. However, evidence that doctors thought she was incompetent at the time of changing a Will can certainly be used to invalidate it later on in Court, if it becomes necessary to do so.
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While a doctor's finding is helpful, in most states only a court can legally declare an individual incompetent, and even that finding is often not sufficient to remove the power to change a will.
It sounds like there may be a need for a court to appoint a guardian and/or conservator. You should contact a local attorney who specializes in guardianship to explore this further.
This information is not intended to create an attorney-client relationship and should be confirmed with an attorney in your area.