Does the sacrifice fall away from the son who has an income and spends on the household equally with his mother, if the maternal uncle sends the mother the price of the sacrifice?

A single sacrifice (Udhiyah (definition)) is sufficient for a man and his household. The sacrifice is incumbent upon the one who provides financially, not on those he supports, subject to three conditions: that they reside with him, that they are relatives or a wife, and that he spends on them, whether obligatorily or voluntarily. As for someone who is financially independent, he is required to offer a sacrifice for himself.