Good, just checking your reasoning a bit to make sure I was not missing something. The transfer that you did back when you purchased the property is the only transfer that ever could have raised an issue with the government (Medicaid folks). However, since it was so long ago it was not and is not an issue for your mother. Since the funds have been outside your mother's name for years Medicaid does not care who holds them.
In fact, anyone can use any money they choose to pay for anything they want for your mother, including a private room, and that is not an issue with Medicaid or her future Medicaid benefits. She just cannot receive cash or have assets over the $2,000 cap.
Your brother holding all the money in one account in his name does worry me a bit. There are several concerns. First, if your brother is in a care accident and kills someone then those assets are fully subject to his creditors to take that money. Second, if your brother dies then those assets will pass to his heirs
by state law or under his will. Third, there is no legal requirement that your brother share any of this money with his siblings after your mother's death.
The safest way for the money to be held is in a trust. It is possible to create a trust, your brother fund it and the money would be protected from his creditors, the trustee would control the money and the trust would specifically state where the trust money goes after your mother passes. There can be some cost to setting up such a trust with a local attorney so it may be cost prohibitive.
If you choose to forgo a trust the account could be placed in the joint names of the siblings. Please remember that this does make the account subject to the debts and potential creditors of all the siblings then. Without a trust type document there is no way to fully protect against all the risk.
I cannot provide you with legal advise. I have provided you with information about the law related to your question. My answer, and any information that you find online, should not take the place of having a consultation with a lawyer in your area to advise you regarding your specific issues.
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