I don't mean to be a marriage counselor, but I would recommend some form of intervention first instead of legal action. Perhaps the parents (from both sides) can be informed and they can talk to the husband. Baka matauhan and the marriage be saved.
Anyway, adultery is the act of a married woman of having sexual intercourse with another man. Concubinage is when a married man shall keep a mistress in the family home, or have sex with her under scandalous circumstances, or lives with her in another place.
If your sister really wanted to take drastic matters, I would recommend doing the following simultaneously. 1) Taking physical custody of the child; 2) Kicking the guy out of the house; 3) filing a criminal case of
Violence Against Women and Children against the husband with the allegation that his infidelity is psychological violence. If he wants to contest custody, let him file the case.
Please note, however, that your sister's legal position will be sorely weakened if she is not physically here to enforce her right of custody. This cannot be exercised by proxy.
The husband's admission, the child's testimony are all evidence. The child's preference is not binding to the court in case a custody case ensues. The standard that the court employs is "the child's best interest". If it can be shown that, in spite of her choice of the father, it is still better that she stay with the mother, then the court will grant custody to the mother.