Is it permissible for a son to hold his mother accountable for the money he sends her, especially if she lies about her need for it and spends it on others while he suffers from debt and financial hardship?

Since you have experienced good treatment from your mother-in-law, you must assume the best about her and interpret whatever she says in the most favorable light. It is not permissible to accuse her without clear evidence. As for those who relay her words to you, they are backbiters, and their action is forbidden to them. Therefore, do not believe them and warn them. Regarding the mother-in-law's right to her son's money, she is not entitled to take from it except what she needs for herself. If her son gives her what she desires, it is a kindness to her, and you have no right to object to that, as long as your husband provides for you according to custom. You should encourage your husband to honor his mother, for that is a sign of his righteousness and will bring good upon you. Your kindness to his family and overlooking their mistakes will increase your husband's love and respect for you.