They know they are half you, half their mother AND they were created in a bond of love (albeit short lived maybe) between you both.
That bond between their parents is now broken, and they may have to endure one or both of their parents berating and belittling the other.
How would YOU feel ?
How would you feel if someone you had to spend time with, keeps sledging your mum. How would you feel if the very circumstances around your creation was referred to as "a big mistake" by one or both of your parents.
Do you want your kids to feel like that ?
They need to see you respect their mother.
It might feel like she doesn't respect you and so it is not always easy to stay calm at changeover time in particular. It is also very easy to sledge their mum when the children are with you and you're talking to them about her. It may also feel ok to speak to your friends about her with the kids in earshot. What if you were the child ? How would you feel ?
Think about what you would like her to say about you to the kids and say that. If you cant manage that, SAY NOTHING AT ALL, until you are able to. When you berate their mother you berate your children. It is destructive criticism indeed - when the children are not even at fault.
Stay cool and calm when they tell you what mum's been doing or what she said, and above all do not be dis-respectful to her in front of the children. When it is time to hand them back to their mum, be punctual, be calm, be polite.
They need to see you honour your marriage or relationship.
It may feel like the biggest mistake of your life as you look back on the wasted time and lost money. It may feel like a train wreck filled with pain and anger.
But in it there was the joint creation of your beautiful children. And above all other things, the relationship surely must have been worthwhile for that alone.
You can honour it by re-enforcing that it was a good time of your life (albeit in the beginning), that you are glad that you had the time with their mum, so that you had a chance to make the kids, and that even though it's now over, there are many times you can look back on and remember fondly.
Photo albums & old videos are a great way to do this, spend time with them looking at old pictures and talking.
Rise above your temporary anger and do something timeless for your children.