Based on the information you provide, your mother may well have grounds for appeal. The facility should have provided her with a Notice of Non-Coverage prior to terminating Medicare. They may have and your mother may not have known what it was or what to do with it. Ask for a copy and information about whether and how it was given to your mother. It will give you information on how to contact the Quality Improvement Organization for your region, which monitors these issues and appeals. You are too late for an expedited appeal but I’d be surprised if you can’t appeal at all. It sounds like you have one or two issues to argue on appeal: potentially lack of adequate notice, and certainly based on what you say whether your mother should have been terminated prior to the full 100 days. For more information, go to the Center for Medicare Advocacy website which provides a self-help package for appealing Medicare skilled nursing facility denials.
For more information about Medicare appeals, go here: https://www.elderlawanswers.com/can-you-appeal-if-medicare-refuses-to-cover-care-you-received--14429.