All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The expiation of breaking an oath is feeding ten poor persons (the food should be from the average food eaten by the family of the person who has made the oath) or clothing ten people giving each one the cloth which covers the Awrah (those parts of the body which must be covered), or freeing one Muslim slave. Whoever can not do any of these should fast three days. Allah Says (what means): {Allah will not impose blame upon you for what is meaningless in your oaths, but He will impose blame upon you for [breaking] what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford it] — then a fast of three days [is required]. That is the expiation for oaths when you have sworn. But guard your oaths. Thus does Allah make clear to you His verses [i.e. revealed law] that you may be grateful.} [Quran 5:89]
Therefore, the mother of this girl is obliged to warn her daughter that she should not take oaths as an easy matter. The condition of taking an oath is a very serious one. Allah Says (what means): {And make not Allah’s (Name) an excuse in your oaths…} [Quran 2:224].
A Muslim should honor Allah and fear Him. Therefore one should not take oaths any time he likes to do something. Allah Says (what means): {And obey not every one who swears much, and is considered worthless.} [Quran 68:10].
If a person makes many oaths, he will most likely fail to expiate all broken oaths. Indeed, this practice contradicts honoring Allah. In short, the girl must expiate for every oath she has broken; her mother can pay this expiation on her behalf, but she cannot fast on her behalf.
Allah knows best.