How do I buy my brother and sister's share of our deceased mother's house?

Don't dare do what you suggested!  Have a lawyer check the title to make sure there are no unreleased deeds of trust, judgments, unpaid taxes, weird easements, or anything else that would negatively affect the title  to the property. Both siblings need to sign a new lawyer-prepared deed conveying their interest to you.    Pay the money at closing once the new deed is prepared and the title checked.