Your mother can leave her half of the house to whomever she wishes -- including her son from the first marriage. However, if she does not legally provide for what should happen to her half when she dies, her half of the house will most likely go to you, your brother, and your mom's son from her first marriage, all in equal shares.

All of you will own the property as tenants in common, which means that if you can't come to some agreement about who lives in the house and how much rent the other owners get, the house will be sold and the proceeds distributed according to the ownership percentages. This is how many tenancies in common commonly end up.