Generally, the Will is going to control here. If it was executed and witnessed within the past 20 years, it is probably a "self-proving" will. The personal representative nominated in the will is probably going to have control over the Estate. However, in many states, the Estate and the beneficiaries can essentially alter the distribution from the Estate with a special contract. You should consult with an Elder Law attorney with Probate experience in the state where your mother was living when she passed away. This sounds like a bit of an emergency, at least for Katie, so please do not wait to seek good legal advice.
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Probably need. Inheritance is not based on need. It is based on the testator's wishes. Katie can consult with a probate attorney to confirm this.
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If the will was properly prepared and signed and the parent had the ability to understand what was being done and was not coerced, it is unlikely that Katie would win a will contest. She should consult an attorney to review the will and advise her of her rights. Maybe her siblings would allow her to remain in the home for a period of time. She may also have a claim against the estate for the value of the care she gave her parents. Again an attorney representing her needs all of the facts in order to advise her.
The above answer is not to be considered legal advice and should not be relied upon as such. You should consult your attorney for specific legal advice as to your individual situation.