The relationship between your ex-spouse and the children caught in between is a very delicate thing.
It took me many years to understand that I have to be "OKAY" with my children talking to and having a relationship with their father. Even though he and I divorced in 93 and he moved to Arizona in 98, he is still their biological father. I never kept him from seeing the children even though he rarely paid child support. I did abide by the visitation agreement and did my best not to let the children see how much it hurt for them to hear from him or say anything good about him.
The children's relationship with the other parent is COMPLETELY different than the relationship you had with the ex-spouse. You have to take yourself out of the emotional equation to see this and make this work for your children.
Today my adult children are 24 and 25 with families of their own and thanks to facebook, both of them have the ability to reach out and speak to their biological father if they choose to. I have complete peace with it and that is a peace that took many years to come about.
My 2nd husband was a much better parental figure than a faithful spouse. After we first split, I would get very angry at him for contacting my daughter and it was very hard to get over this hurt. My mind kept saying "he hurt me, why does she talk to him knowing he hurt me?" But I had to let this go as well. I am not sure how much they interact but my daughter is grown and #2 did walk her down the aisle and was there for many milestones in her life. He was a great surrogate father to my children that were left with no male figures in their life on a daily basis.
My father and my brother in law were always around but a daily father figure in the home is what I am referring to. My children definitely can say they were raised by myself and my parents and for that I will always be thankful.
Every relationship is precious and children should know their parents if at all possible or it is not an issue of health/well-being. So the next time your child says something good about their biological parent, put on a smile, say a silent prayer for strength/courage in the moment and show God's love even to the ex's who have hurt us. It helps a lot to pray for the relationship to be healed.
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