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The terms of the trust will control the appointment of a successor trustee or the termination of the trust.
With regard to the trust for your brother's and your benefit, it should not be impacted by the appointment of a successor, as provided in the terms of the trust.
If the trust has no provision for a successor to your mother as trustee then you may have to petition the probate court if the term of the trust require a co-trustee in addition to the bank.