This sounds like an awful situation. You should know that, unfortunately, it is not uncommon. It also does not appear to be a legal problem, at least not yet.
A power of attorney (POA) gives an agent the authority to make financial and medical decisions on behalf of someone else. It does not give them power to make decisions over how they live, whom they see, etc. I understand that your sister is making these decisions for your mother, but it is not as her POA agent. Your mother has the legal ability to disregard her daughter's wishes. She may decide not to, and this may be because this daughter is caring for her and she wants to keep the peace. Mom also may be physically limited enough that you have to go to her and, if your mom is in your sister's house and your sister doesn't want you there, you are subject to your sister's wishes in regards to her own home.
If you want to see your mother, she either needs to come to you, or live somewhere where the owner of the property would allow you to visit her. Legal guardianship powers would allow you to make decisions about where your mother lives and whom she sees, but being appointed guardian is an involved court process that requires a showing that your mother is so incapacitated that she is unable to make reasonable decisions for herself. Your sister also may try to become appointed guardian, and then a court would have to decide which of you is more suitable. If you are concerned that your sister is mistreating your mother or mishandling her financial affairs, there are legal actions you can take to protect your mother. Otherwise, the legal system doesn't have much to offer you for solutions.
My non-legal advice is to try to mend fences with your sister, at least temporarily. Your mother may not be around, or mentally available to you, much longer. If apologies and trying to get along with a difficult person will bring you some time with your mother now, it may be worth it. You're a bit at your sister's mercy here, which is a hard situation, but focusing on your mom may help diffuse some of this tension. With her health problems, the loss of her husband and the recent loss of a child, it sounds like she could use both of your support, and as much peace as you both can muster. Good luck.
Legal advice depends upon the particular facts of a given situation. Please use my answers as general information but not legal counsel.
This is an unfortunate situation without an easy resolution. Family mediation might be the best way to try to mend the problems within the family, but this will only work if everyone agrees.
If an amicable resolution is not possible, then the sibling needs to hire an experienced Elder or Guardianship Attorney to discuss the available options. The first question will be how advanced is Mom's Ahlzteimers. If she is still competent she can revolk the Power of Attorney and appoint one of the other children.
If Mom is no longer competent, then the situation becomes much more complex. If the siblings suspect that Mom is being mistreated, then they can contact the Illinois Department of Aging and request an investigation of any Elder Abuse. The investigators are usually very good and persistent. If there is abuse, then a cause of action exists to remove the Mom from the current daughter.
If there is no obvious abuse the situation is difficult and expensive to resolve. In Illinois agents properly appointed under the Illinois Durable Power of Attorney act cannot be replaced by a court appointed guardian unless the Court specifically finds that the agent is not acting in the best interest of the principal. Illinois law is designed to respect the choices made by the individual while they were still competent and not to overrule them without strong evidence of a breach of the fiduciary duty. While you would think that being deprived of visitation with the daughter would automatically qualify, it probably doesn't. If the current agent feels that the contact with the sibling has a detrimental effect on the Mother, the Court may find her justified in limiting contact with the Mother. So while the sibling may be left with no alternative but to file a guardianship action, the sibling should be aware that such a course of action would be expensive and very likely could be unsucessful.
Disclaimer. The information contained in this answer is provided for informational purposes only, and should not be construed as specific legal advice, further is not intended and it does not constitute or create an attorney-client relationship between The Law Office of James C. Siebert & Associates and any recipients. No recipient of this answer should act or refrain from acting on the basis of this answer without seeking the appropriate legal advice on the particular facts and circumstances at issue from an attorney licensed in the recipient's state. Under Illinois ethical rules answers to questions might be considered as advertisement and therefore please consider the answer to the question is ADVERTISING MATERIAL.
Q: "What can the sibling do? (the one being kept away). How can this be legally resolved? "
A: Consult with an elder law/probate counsel... seek guardianship.
This is not legal advice. I am not your lawyer. You are not my client. You cannot rely on my response to your question. My response to your question is probably worth exactly what you paid for it. You don't get to sue me for anything. If you'd like to sue me, well you have to hire me first. Here's how you can hire me! #1 Call: 1-888-463-2843 #2 Email: email@example.com #3 See me on TV! www.woodtv.com - go to the Ask the Expert tab! #4 Listen to my radio show (2 full hours every week!) www.woodradio.com - go to the podcast section.