Is it permissible to take the full amount for the daughter without the knowledge of her mother, who obliged her to take half of it even though she is not in need of it?

Filial piety towards one's mother is an obligation and one of the best acts of drawing closer to Allah. This includes spending on her if she is in need. If the mother is financially secure, she is not entitled to any of her children's money without their consent. Therefore, you are not obligated to give your mother what you promised her as long as she is not in need. However, you must show her piety, satisfy her, and avoid anything that displeases her. It is better to give her what does not harm you, especially since you promised her. Imam Malik indicated that appeasing one's mother and removing her displeasure by any means possible is preferable.