I'm going to give an example for my question:
If my mom had a irrevokable trust drawn up and it is supposed to distribute her property equally between myself and my brother when she dies and there was a provision in it stating: DURING MY LIFETIME I MAY APPOINTMENT ANY OTHER TRUSTEE TO ACT WITH ME OR IN MY PLACE BY ASSIGNED WRITING. If she appointed my brother to act in her place, would that make him the new trustee? Could he benefit any more than me when my mother passed? Would this make him in charge? Could he take possession or occupy the home? OR, AM I READING TOO DEEP INTO THIS AND WOULD THE TRUSTEE ONLY FULFILL THE TERMS OF THE TRUST?
Thanks so much for your help!

Its hard to answer without knowing the terms of the trust. But appointing a beneficiary of the trust as the trustee does not mean they will get anymore out of the trust then defined by the trust agreement. The only extra he might get is reimbursement for any expenses he incurs as trustee.

The trustee would be in charge of managing the assets of the trust and distributing those assets according to the terms of the trust.