His mother swore that she would never give him money, then she wanted to give him

There is nothing wrong with taking money from her out of respect for her. In this case she has to offer expiation (kafaarah) for her oath, because she did not fulfil it. Kafaarat al-yameen (expiation for an unfulfilled oath) means feeding ten poor people with the average food that your family eats, or clothing them, or freeing a slave. What is obligatory in feeding is half a saa’ of the staple food of the country, such as dates, wheat, etc. It is equivalent to approximately one and a half kilograms of rice, which should be given with something that can be eaten with it, to one poor person. It is obligatory to give to ten different people. If you can find a family of poor Muslims composed of ten members, or two or three families who numbers add up to ten, and you give them fifteen kilograms of rice, along with some meat, for example, this will be sufficient. Or you can distribute to them what is needed for ten lunches or dinners already cooked, of the food that an average person needs for lunch, and this is sufficient. Clothing means that which is needed to cover the ‘awrah for prayer. If your mother is unable to feed or clothe poor people, or free a slave, then she has to fast for three days, because Allaah says (interpretation of the meaning):

“Allaah will not punish you for what is unintentional in your oaths, but He will punish you for your deliberate oaths; for its expiation (a deliberate oath) feed ten Masaakeen (poor persons), on a scale of the average of that with which you feed your own families, or clothe them or manumit a slave. But whosoever cannot afford (that), then he should fast for three days. That is the expiation for the oaths when you have sworn. And protect your oaths (i.e. do not swear much)…” [al-Maa’idah 5:89]  

We advise you to avoid doing anything that may make your mother angry. She did not make an oath except for you were disposing of the money in a manner of which she did not approve. May Allaah help us and you to do all that is good.