As the successor trustee of my late mother's estate, do I have the power to say who can or cannot live in my mother's house?

Yes, and good luck.

The Trustee can evict persons without a right of possession.

The executor has little power. Since real estate is involved, you must probate the Will and the court will appoint an administrator of the Will [normally the executor][trustees only exist for Trusts] who can then petition the court to sell the house or can get title transferred. If your sister already owns any portion of the house, you can not evict her. If she does not, you can give her a 3 or thirty day notice [if she was paying rent but has not paid to the estate, use a 3 day notice]. If she is an heir, once the Will is probated she becomes an owner and owners can not be evicted by other owners nor do they have to pay rent. If the court ordered the sale of the house, then the funds are split as stated in the Will. Notify the assessor's Office of the death; it should not result in any reassessment. Nolo Press has several good books on the subject; it is in your local library.