Why do you have to go through probate?

You are merely a trustee, who is responsible for the assets in the trust. The trust assets should be comlpetely immune from probate and all you need to do is to follow the trust provision to distrubte the interests and principles and make sure it terminates as the trust agreement says. As for the grantor's other assets, it's none of your business unless he as a pourover will that instructs the executor to pour all of part of his/her estate into the trust.