I thought of many things as I read your post. Your boyfriend probably just doesn't feel like you are a family because other than your shared children, you and he have no permanent connection. Being a dad is not the same as being a husband. Does he have responsibilities to you and the kids? Does he need to love you and be faithful to you? Of course he does. But making a family with children outside of a marriage is a huge risk and many men just don't believe it's a permanent commitment.
You both need Jesus in your lives. He is the only one that can heal and make sense of this mess. I'm going to pray for you now and will continue to pray. Please pray and seek God for your life. Read the Bible, especially the book of John. Then look at these scriptures:
Love is Awesome
“Love suffers long, and is kind; love does not envy; love does not promote itself, is not puffed up, does not behave badly, seeks not her own, is not easily provoked, thinks no evil; does not rejoice in iniquity, but rejoices in the truth; bears all things, believes all things, hopes all things, endures all things. Love never fails” 1Corinthians 13:4-8
Marriage is a Covenant – so God is Part of Every Marriage
“… the LORD hath been witness between you and the wife of your youth, against whom you have dealt treacherously: yet is she your companion, and the wife of your covenant.” Malachi 2:14
God Joins the Couple Together so their Sexual Intimacy is not Sinful
“What therefore God has joined together, do not let man put asunder (separate).” Mark 10:9
Pray, seek God, read His Word and Commit yourself to the Lord. We'll keep praying and see what God does.
Father, In Jesus' name, I ask that you draw MotherOfTwo to You and intervene in her situation with her boyfriend. His adultery is hurting her and their children. Lord we know that you have a plan and an answer for her, if she is obediant to you. Bring salvation to both of them and convict this man of his sin and show him the hurt and pain he is causing the family that he created. I pray your blessing on this home and we seek your will in all of this.
In Jesus' name, Amen.
I will continue to pray.