The Christian God is a God of grace and mercy. He wants all of us to come to him and he turns away none who do. He knows we are weak and “sinful” but loves us all the same. All mothers and children are precious to God - no matter what their background. Indeed God is often described as the “father to the fatherless” (Psalm 68:5).
Any Bible believing and Bible following church should welcome anyone who comes to them and wants to find out more about God (no matter what their background). They should help you as a mother and help your children to know of God’s love in Jesus. After all Jesus is the one who welcomed the social outcasts of his day such as tax collectors and sinners eg see Luke 7:36-50. God’s church consists of people from many varied backgrounds, but we are all one in Christ Jesus.
There are many single mothers in our society, and any church should welcome the mothers and their children (no one would know who the fathers are). Even if you tell that your children have different fathers, this should not affect how Christians treat you. Alas, not all people in churches yet realise that our God is a God of grace and mercy, and not legalism. Alas, such people do not love others in the way that God wants them to. My prayer is that God would keep you from such people and put you in touch with other Christians who are keen to show God’s gracious love towards you and your children.
I do not know where you live, even so, I have spoken to the Sydney branch of the Mothers Union, and they said they’d welcome your call or email to help you find a loving church in your area, even if outside of Sydney. The Mothers Union was founded a while ago, so most of its members are women whose children are now adults, but these women would be keen to serve as adoptive grandparents to your children and help you in your family life. Either email or phone Monday to Friday 10:00am to 2:30pm . Phone/Fax (02) 9267 8372, email@example.com . If you live outside of Australia, I’m sure they can still help you find a good church.