Can a trustee use Trust money to purchase income property to benefit himself and only one of the beneficiaries?

It is most likley not legal:
1) A trustee is bound by the terms of the trust, so if the trust makes you and your sister also beneficiaries with your brother and gives you all more or less equal benefits or rights in/to the trust property/assets, the trustee may not ignore that and favor one benefiriary over another.
2) A trustee is also bound by a "fiduciary duty," or duty imposed by law to be loyal to *all* beneficiaries and to NOT engage in "self-dealing," or benefitting himself at the expense of beneficiaries.
 
Unless there is some provision in the trust justifying or authorizing this specific behavior, as stated, it is likely illegal. A court could order certain actions to be undone, such as requiring them to sell the building and put the proceeds into the trust and distribute them fairly to all beneficiaries; it could also order the trustee to repay out of his own pocket any amounts he improperly took out of the trust or profits improperly made; and court could replace the trustee.
Ideally, you and your sister should jointly hire a trusts and estates attorney to bring a legal action on your behalf. If you truly cannot afford one, you can each file an action in  chancery court (a part or division of county court) for an "accounting" to have the court look into what has been going on and hold the trustee accountable for his actions. You would have to each file an action, which the court might then combine or consolidate, since while you can each represent yourself "pro se" (as your own attorney), neither of you can represent the other. (Obviously, if you want to do this and your sister does not, you can file you own action without her doing so and vice versa.) You would name the trust and the trustee in the lawsuit. Dowload or buy a copy of your state's rules of court and also contact the clerk of the chancery court's office for filing instructions.