Your ex has now become your worst nightmare. As the custodial parent of the children you share and with a toxic personality to boot he or she now has the ability to make your life hell. The more that you protest against their inappropriate ways the worse they may become. Toxic people are self centered and do not care about the feelings of anyone else nor do they understand the word "fair". So how are you to deal with this person for the next several years?
Keep low contact. The less that you talk to your toxic ex the fewer chances they have of making you mad or instigating another disagreement. While some interaction is necessary due to the children you share, keeping it to a minimum is best. As the children grow older there will be less and less need for contact between the two of you.
Use email rather than the phone. In most cases communications between a divorced couple are better handled through email. When speaking on the phone or in person it is much easier to get drawn in to an argument. Emails are more emotionless and will also provide you with a record of what information was exchanged should you need proof in the future.
Silence can be golden. Toxic people often attempt parental alienation by turning their child against the non custodial parent. No matter how difficult it is or what horrible things your ex is telling your child, you must refrain from saying anything bad in front of them. Children should not be brought into the middle of wars between parents.
Spotlight honesty. If your child comes to you repeating something that your ex has said and asks if it is true, honesty is the best policy. Depending on the topic and your child's age you will want to answer in an appropriate manner. Stay calm and stick to the facts. You have every right to correct lies that your toxic ex has told your children.
Keep your emotional distance. When you absolutely must speak with your ex try to remain as emotionally uninvolved as possible. Toxic people like to push buttons and make others squirm. If you do not react to their provocation it will make the interaction less stressful.
In extreme cases where your ex is so toxic that they are a danger to your child's physical or emotional well being, you might need to take them back to court and fight for custody. As long as you have evidence to back up your claims a judge will probably be willing to hear your case.