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No matter how upset you are, never involve your child in the animosity. Never assign fault to your ex for the separation. Speaking negatively about your ex will not only risk the child lashing out at them or you but will also cause the child serious tensions and a feeling of being torn between the two of you. If you learn that your ex is speaking negatively about you in front of the child, be the bigger person and don't retaliate in kind. Explain to your child that your ex is under pressure from the separation and is doing their best to get through it. Almost as important as refraining from disparaging your ex is encouraging your child to see your ex in a positive light. Say nice things about your ex whenever possible to demonstrate to your child that the end of your romantic relationship has not ended your co-parenting relationship and respect for each other. Encourage your child to appreciate the skills and parenting effort of your ex by saying things like "Isn't your father's cooking great?" or "Your mother did a great job coaching your little league team." It can be difficult to adjust to seeing your ex with a new relationship but you'll have to accept that this person will be a significant part of your child's life. Your child is likely to take cues from your perception so showing your animosity toward them could lead your child to disrespect and resent them. This will not only cause stress for your ex and their new relationship but also for your child. Try to compliment the new relationship. Ask your child questions like "What is dad's new girlfriend like?" and seem interested and impressed. Tell them explicitly that they need to respect the new relationship as an authority figure. Say something like "Remember, mom and her new husband are the adults of the house. Show them both the respect that you would show me." If your child dislikes the new relationship, give them the chance to vent their frustration but encourage them to adapt to the new situation. Try to relate to them by saying something like "This is hard on me too." Using them as a messenger will put your child in the middle of your conflict and force them to feel the tension of your relationship. Unfortunately, this is a common mistake for separated parents that don't want to deal directly with each other, but you don't have to make it too. Find more productive ways to communicate like email, phone, or even talking through lawyers.
Keep negative thought to yourself. Compliment your ex. Encourage your child to respect your new ex's new relationship. Communicate directly with your ex.