Legal Question in Wills and Trusts in California

Probably. Both the trust document and the power of attorney would have to specifically authorize the trustee to delegate to an agent. And fiduciary responsibilities of trustee (such as decision making) cannot be delegated.

That is correct. Because a trustee is a fiduciary to the beneficiary, they cannot delegate their powers. It is kind of a silly rule when the trustee and the beneficiary are one and the same, as is usually the case in intervivos trusts, but the legal theory behind it is sound. If you make someone a trustee you are granting them the ultimate authority over the assets you place in trust. You wouldn't want a legal rule that allowed them to then give that authority away. So in order to give you authority, your father would have to amend the trust to name you as co-trustee, or if permitted under the trust instruments, make a distribution out of the trust into a new account you can both sign on.