As trustee of a Living trust, can I directly distribute my brother's assets to his wife, even if he died without a will, or must I go through Probate?

If the trust document says that assets are to be distibuted to your brother's wife upon his death, then you can follow the terms of the trust without need of probate.  If the trust terms state that any trust assets should be paid to your brother's estate, then you could distribute them to his estate but then you or his wife would need to file probate.  Trust assets are not probate assets.  Estate assets, or any assets not owned by the trust that your brother owned solely in his name, are probate assets.  Only probate assets require probate process.  Hope this helps.