Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
If the situation of this woman is as mentioned in the question, that she does not pray, is not interested in religion, and practices sports while listening to music and does not wear Hijab, then we advise you not to approach her in anyway.
We advise you to abide by the advice of the Prophet (Sallallahu Alaihi wa Sallam) in choosing a wife. Al Bukhari reported in his Sahih that Abu Hurairah (Radiya Allahu Anhu) narrated that the Prophet (Sallallahu Alaihi wa Sallam) said: "A woman is married for 4 things: she is married for her wealth, for her honourable lineage, her beauty and her religion. Marry a religious one you will prosper."
You have to know as well that a group of scholars are of the view that a person who does not perform Salat (prayers) is a Kafir and apostate. Therefore, according to this opinion, it is not permissible to marry a woman who does not perform prayers, and there is no good in her.
Dear questioner, you have to fear Allah and to seek for your children a righteous mother who could bring them up according to Islamic principles, an education that would please Allah, the Most-High.
Allah knows best.