Your description raises far more issues than your question covers. Much depends on your mother's level of competence and vulnerability. Her independence and self-reliance should be respected and preserved as long as possible, but if the companion has become abusive, she must be protected and an intervention is urgent. Whether you must pay the taxes on the house you now own should be the least of your concerns. Your mother needs independent legal advice, and you may as well. The expertise needed is elder law. If you do not know such an attorney, go to www.naela.org for a referral.
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This answer is offered as a public service for general information only and may not be relied upon as legal advice.
Assuming your mother is competent she should retain an attorney locally who will help with the elder law issues. She also should do some estate planning to clearly spell out what she wants to happen with her remaining assets and also to appoint legal representatives for her medical and financial issues. If you own the property you probably are liable for the taxes. However, you are also within your rights to charge the companion for rent.
You and your 6 siblings each own an undivided 1/7th interest in the home as joint tenants. Legally you are responsible for payment of the taxes and maintenance of the property. As owners you may evict either or both of the present occupants. Each of them is free to vacate the property at any time. Having said all that, your question raises a number of issues far more serious than what your legal rights and duties are with respect to the property.
Since the live in has been there for 21 years, it appears from the tone of your question that this has been a problem among your family for a rather long period of time.Your Mother's children have the absolute right to make Health Care decision for her as a matter of law for your mother, if she is medically certified to be unable to make those decision for herself. I would suggest that since there are 7 of you that you urge your mother to consult with an experienced Elder Law attorney who would inquire as to whether she has both a Power of Attorney and a Health Care Power. It is not a wise choice to leave those matters to chance, or to end up with 7 persons being involved and having to make a unanimous decision on every decision, plus a majority vote may not be acceptable to either a financial institution or a health care provider.
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Mr. Geisenberger is a Pennsylvania-licensed attorney only. The information is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation. Answering this question does not in any way constitute legal representation. Contacting Jacques H. Geisenberger, Jr., P.C.,does not constitute legal representation, nor is any information you provide protected by attorney-client privilege.