Can my sister prevent me from living in my mother’s house if she is the executor of my mother’s will and is living in her house too?

That depends on several factors. As executor, your sister has very little power until and unless she is appointed administrator of the Will by the court once probate is filed. She has no more right to live in the house than you, and the estate could charge her for rent while she lives there. She probably can not file an eviction action as mere executor. You need to speak to her and find out why she wants you out and on what legal basis and why she is entitled to live there. You might need a quick letter from a local attorney telling her she can not kick you out without her also leaving.

If your sister is the executrix, she has a fiduciary duty to administer the estate for the best interests of ALL beneficiaries. Does the will name both (all?) of you as beneficiaries? Equally? Has the will been submitted to court with a petition for probate? Does she plan to sell the property in order to distribute the estate? If so, the house will have to be sold free of tenancy. With these questions, it's hard to give an answer. However, if there are just the two of you and you are equal beneficiaries, she and you must decide whether you want to take title as tenants in common, each owning half, or to sell and eventually (with court approval) share the proceeds. Please note that (unless there is a trust) your sister is not the executrix until the court says so, and Letters Testamentary? are issued. Until then she has no power to act, other than to preserve property of the estate.

In short, yes.