What is the ruling on sending money to one's mother to help her with living expenses, and is that considered charity (sadaqah), and does informing one's wife nullify the reward for this action?

If the mother is poor, the money sent to her is an obligatory maintenance. If she is rich, it is a gift and an act of devotion. In both cases, spending on her carries a great reward. It is better to conceal this from the wife, unless there is a legitimate Shariah interest, so that it is closer to sincerity and acceptance.