Is it permissible to travel for marriage without the mother's permission, knowing that she disapproves and fears being left alone with my young siblings, and my wife and her family are being harmed by the delay?

If the mother will be safe and there is no fear of her being lost or neglected, then there is no harm in traveling without her permission. However, seeking her permission and her being pleased is more complete. But if there is fear of harm befalling her and there is no way to prevent it, then it is not permissible to travel except with her permission. At that point, either the wife must be patient or divorce. Allah Almighty says: "But if they separate [by divorce], Allah will enrich each of them from His abundance. And Allah is ever Encompassing and Wise." And if the matter is merely related to obtaining residency, then he should strive to acquire it so he can travel and then return to his mother.