Is standing with orphans against their abusive mother considered a disobedience to her, and what is the ruling on not allowing her to travel with us to prevent her from harming them?

If what you mentioned about your mother is true, then her behavior with her grandchildren resembles madness and is not a method of discipline. Grandchildren must be protected and harm must be warded off from them. Preventing your mother from oppressing them is a kindness to her, for the Prophet, peace and blessings be upon him, said: "Help your brother, whether he is an oppressor or oppressed." Helping the oppressor means preventing him from oppression. If there is no way to ward off her harm except by preventing her from traveling with you, then there is no blame, and that is not disobedience. However, it is better to placate her and arrange with one of the siblings for her to stay with him. The grandchildren should also be directed to avoid what provokes their grandmother's anger, especially given her old age.