Can she leave me the house when she passes without having to look for my stepdad’s kids?

You do not state whether your step-father had a Will. Assuming he did not have a Will, his spouse and his children would be the co-owners of the property by the rules of descent and distribution at his death. Your mother, as spouse, has a 50% ownership interest in the house. She can create a will that would give you her entire interest at her death. She should see an attorney to create and execute a Will. She should also see an attorney to evaluate whether or not the facts and circumstances of her residing in the house since her husband's death support bringing an action for adverse possession. A successful adverse possession suit could result in her establishing ownership of the entire ownership interest in the house.