Is your brother disabled, receiving Social Security Disability or SSI or in any way limited in function like this? If so, that is the exception under which they cannot put a lien on your mother's house, if she does not have enough assets to cover her care out of pocket and they are trying to sign her up on Medicaid. That's the entity that will pay the bills after she has exhausted her days of Medicare paying (if any) and needs to stay longer, and no longer has the assets to do so without Medicaid. They'd put a lien on the house and take whatever is owed them after her passing. But they do not take the home if it is also the home of a disabled adult child, I believe. Your nursing home social worker, and the people at the Medicaid office will be able to help you a lot with these issues. But there's no being "crafty" or protecting your assets at this point.
If your mother had deeded the home over to you and your brother say about six or seven years ago, you'd be the owners of the home and they would not consider it as an asset of her estate. Otherwise, they go back several years, about five or more, and look to see if there's been any transfer of assets in an attempt to defraud Medicaid. She would not be eligible until the value of all assets, including something she tried to get rid of in the last five years (the "look back" period) was spent.
If your mother has to have nursing home care, there's no reason she should not pay for it until her assets are depleted. If she'd fallen over suddenly and passed away, you'd own her home free and clear. It's a gamble you take that your elderly parent will not need expensive care in her final years. But if she does, that's the reason she saved and worked and bought the house in the first place, to take care of herself, not to give it to you and your brother.