No probate should be required (Will provides personal items to two of three children, remainder of estate to trustee of trust).
You are no required to give notice of the will per se. You are required to give the appropriate notices under PC 16061.7 for any person named in the trust, and my guess is the will and trust are consistent with each other. If after you give the required notice under the trust someone requests a copy of the trust documents the will should be provided as well.
I agree with Attorney James. I would simply add that it is not clear from your limited summary is there are any assets that need to pass through probate. If there are, then they would go to the trust, but probate would be necessary to get it there. It would not hurt to consult an attorney if you have any questions.
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Attorney James has given you a good answer. It isn't clear from your fact summary if the Will has been lodged or, if not, who has the Will and the duty to lodge it. You need to contact a local probate attorney to discuss this matter in greater detail.
Personal Injury Lawyer
I agree with the answers above and specially with the recommendation that you consult with a competent probate attorney who will be able to review titling issues and determine exactly what asset are subject to the trust and/or will and will be able to advise you accordingly.