Is it permissible to travel for work and leave one's elderly mother alone, knowing that she agrees to it?

Staying with and caring for one's mother is one of the greatest acts of devotion, and it may even be superior to jihad, especially if the mother is elderly. If you are compelled to travel, try to take her with you if that does not cause you hardship. If you cannot, then leave her with your children and wife, and hire a trustworthy maid for her if the wife does not care for her, and communicate with her by phone, and invite her to visit you if possible.