Is a mother's coercion of her son to swear an oath considered an excuse for not offering expiation, or does it not fall under the definition of coercion? And is it permissible to offer clothes owned by the swearer as expiation for the oath, and what is the required amount of clothes to be offered?

There is no expiation for one compelled to swear an oath. However, if you were not compelled by a legitimate form of duress, and you had the option not to swear, then expiation is due upon you if you broke your oath.

The expiation for an oath is feeding ten needy persons, or clothing them, or freeing a slave. If one cannot find any of these, then fasting for three days.

If you do not have money for food or clothing, then you should fast for three days. You are not required to wait until you have money, nor are you required to use the clothes you need as expiation, nor to take from your mother's clothes.

It is a condition for clothing the needy person that it be sufficient to cover for his prayer, such as a shirt or an izar (lower garment) and a rida' (upper garment) for a man, and a full-length garment and a khimar (head covering) for a woman. A pair of trousers or a jacket alone is not sufficient.