You meet, you establish a relationship, you have kid(s), you breakup. When children are involved in a failed relationship, the effect on them can be profound. Still, the adults that couldn’t make their relationship work tend to focus themselves. The parents in some cases may move on and acquire a new significant other. Just because the parents broke up and allegedly moved on, the issues that led to that end result do not disappear.

Keep issues between you and your ex between you two.
A new mate does not take away the HATE. You would think that because your ex has someone new, that would resolve any issues that the two of you had to cause the split. At times those issues end up transfering to the ex’s new boo (Urban vernacular for significant other). They in turn can decide to get emotionally involved and react negatively to the other parent.
If you allow for your new boo to disrespect your child’s father/mother that is positively involved in their child’s life. You are a sorry ass example of a parent/role model.
They tend to bad mouth said parent and treat them with disrespect. Not because of first hand experience but because of being third party mad based off of what they were TOLD. This is not good for anyone involved in such a situation, especially the children.
If you allow for your new boo to disrespect your child’s father/mother that is positively involved in their child’s life. You are a sorry ass example of a parent/role model. Whatever issues you may have had with your ex. Is between you and your ex. There’s always two sides to every story and unfortunately they often don’t line up with one another. A bad relationship does not negate a GREAT parent. So just focus on your new relationship and what’s best for the children. Better yet, JUST LET ALL THAT PAST HURT GO! When you don’t. All you’re doing is damaging the kids.
If you are the new boo. You have to know your role and learn it. You are an addition, not a replacement. So govern yourself as such. If you can’t respect the other (Positively involved) parent of the child. YOU DON’T DESERVE RESPECT YOURSELF.