“My mother’s will stated that when she died her house would be sold and the profits divided between me and my sister. My half was to go in a trust fund for me and my sister gets the other half outright. My question is: Can I buy out her half and obtain the property for myself?”
If it weren’t for the trust, the answer would probably be yes. Normally, when property in probate is being sold, the heirs are not excluded from bidding, meaning that one or more of the heirs could buy the property from the estate. Keep in mind, though, that probate sales are usually court-supervised, and have a lot more rules than your ordinary property sale. You should contact the attorney for the estate to find out exactly how the procedures work in your case.
However, your share of the inheritance is being held in trust, so unless you wanted to buy the house yourself (and have half of the money you paid held in trust for yourself), it would be your trust and not you that would have to buy the house. Unless your trust has other sources of money, I don’t know where it would get the cash to buy your sister out.