If the house is sold, the proceeds should be divided three ways with your mother receiving a third. This is also true of any rental income. A key issue after your mother’s death is whether she, your sister, and your brother-in-law own the property as joint tenants or as tenants in common. If they own it as joint tenants, upon your mother’s death her interest will automatically disappear and your sister and brother-in-law will be the sole owners. If they own it as tenants-in-common, your mother’s one-third interest will pass to her estate and will be distributed according to her will, or if none, equally to her children. Whatever the ownership interest, your sister and brother-in-law can still distribute the proceeds according to the original agreement, but with nothing in writing that agreement is probably not legally enforceable.
For more information about joint tenancy, click here.