All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Whoever vows to fast three days has to fulfil his vow and fast as the Prophet said: "Whoever vows to obey Allaah has to obey him." [Al-Bukhari] As regards vowing not to speak to people, then it should not take place and you are not obliged to fulfil it because not speaking to people is not an act of obedience. Ibn 'Abbaas narrated that while the Prophet was preaching there was a man whose name was Abu Israa'eel, who vowed to stand and not to sit, not to stay in the shade but be exposed to the sun, and to fast and not to speak. So the Prophet said: "Order him to talk, to shade himself, to sit and to continue his fast." [Al-Bukhari] So the Prophet ordered him to talk because not speaking is not an act of worship that is acceptable to make a vow about.
Concerning whether or not one has to expiate for vowing not to speak, there are two opinions. The most correct opinion, however, is that there is no expiation, this is the view of Imaam Maalik because the Prophet did not order Abu Israa'eel to expiate for his vow.
To conclude, this woman has to fulfil her vow in relation to fasting but does not have to do so in relation to her vow not to speak, and she does not have to expiate for it.
Allaah knows best.