We are truly saddened to hear about the struggles your sister's family is facing, and we are here to support you all in prayer and truth.
Firstly, we want to remind you that change in people comes from the Lord. Only the Holy Spirit within us do we not fulfill our bodies desires. The fruit of the spirit will be shown in a persons life, so it is possible to see a change in the desires of the flesh, such as flirtation to the opposite sex that is not our spouse. If your brother-in-law is continually participating and pursuing in flirtatious actions with others while being married, then he must stop now and repent to those he has targeted or fantasized as well as the Lord. For it is written, "But I say to you that whoever looks at a woman to desire her has already committed adultery with her in his heart." The Lord will not leave him in this way though, as He promises in 1 Corinthians 10:13 WEB, "No temptation has taken you except what is common to man. God is faithful, who will not allow you to be tempted above what you are able, but will with the temptation also make the way of escape, that you may be able to endure it."
We also pray for your sister, that God would give her the strength and wisdom to handle this situation. It is commendable that she has been confronting her husband, but we want to encourage her to do so in love, prayer, and with the support of fellow believers. We encourage her to reveal all to the Lord in prayer and her husband. For the Lord is already aware anyway. Nothing is hidden. As Matthew 10:26 WEB, reminds us "Therefore do not be afraid of them, for there is nothing covered that will not be revealed; and hidden that will not be known." The Lord is aware what occurs in private. For it is written, "He reveals the deep and secret things; he knows what is in the darkness, and the light dwells with him." Daniel 2:22 WEB
It is an unpopular topic and may even sound harsh, but just as it is important your brother-in-law must be faithful to your sister, it is equally important that your sister remain faithful, support, and obey her husband as the church obeys Christ in all things.
However, there are exceptions. If adultery is committed then it is reasonable for divorce to occur, but we pray this is not the case and will not become. For Jesus taught us these things in Matthew 19:8-9 WEB, "He said to them, Moses, because of the hardness of your hearts, allowed you to divorce your wives, but from the beginning it has not been so. I tell you that whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and he who marries her when she is divorced commits adultery."
We also want to remind you that God can work miracles. It is not too late to see repentance, but warning has been made this is serious through this prayer request. It will be subject to accountability. We advice your sister to seek to the Lord, be open, and faithful in prayer and in all things to her husband. We encourage and pray that they seek their family to the Lord Jesus Christ. We pray for the unsaved household of your sister to be saved. As well we pray for your sister to trust in the Lord. For it is written, "Trust in Yahweh with all your heart, and do not lean on your own understanding. In all your ways acknowledge him, and he will make your paths straight" Proverbs 3:5-6 WEB and "But seek first God’s Kingdom, and his righteousness; and all these things will be given to you as well." Matthew 6:33 WEB.
May God lead her and bless you all with victories over all the desires of the flesh to please Him only. We pray for your families desire and love to only be for one another so that all will see a marriage that the will of God is fruitful for when He is the center of marriage. We pray for that all the desire in the heart of your brother-in-law would only be his spouse, your sister. If he and your sister have been saved by the grace of Jesus Christ, then may he and your sister feel the Holy Spirit within convicting them to reinforce the changes of clarity and power over sin that occurs by believing in Jesus Christ as Savior. Please read what the following scripture says regarding Jesus Christ. From Acts 4:12 WEB, "There is salvation in none other, for neither is there any other name under heaven, that is given among men, by which we must be saved!"
It is only by the name of Jesus Christ that we have access to God. If you have not made the decision and have the assurance within you must be saved by only believing in Jesus Christ as Savior, then seek to Him in this moment of praying. Then seek discipline and baptism in a local church. In Jesus name. Amen.
Finally, we would like to remind that the focus is always on Jesus Christ and not ourselves when we pray. Jesus has been invited in the heart of your sister and her husband then gain power over sin by only believing in Jesus Christ. Pray specifically to the God the Father to Jesus Christ and His Holy Spirit. Always pray in Jesus' name for it is only by the name of Jesus Christ that we can approach the throne of God with our supplications.