Do you own this as joint-tenancy, as members of an LLC, or some other structure? Is there anything in writing to suggest that one of the siblings can force a sale?
Do you have equal ownership (one third each)?
Have you previously been compensated in any way (free/reduced rent, salary, preferential returns, etc) for managing the property?
Do you have the cash flow, and/or would the income from tenants, support a mortgage so that you could pay out one or both siblings and take more or complete control of the property? (This is probably the best approach to keep the property and get this person out of your life)
This is the beginning of negotiations.
I absolutely agree that this person needs to be out of my life. The audacity... does not baffle me as this person is a POS coward that he is, only daring to ask after our father passed