By "check him" I assume you mean confront him on the issue.
You are talking about the mental and emotional health of the kids. Without knowing all of the particulars of your situation it is difficult to answer with certainty. I can say that without extenuating circumstances it would be appropriate, otherwise you will forever be doing damage control with the kids.
Attitude and approach will matter.
PR 15:1 A gentle answer turns away wrath, but a harsh word stirs up anger.
I am not sure if it would feed into this behavior for her to say something to him or if it would make him aware that his words are being repeated by the kids. But as far as God's response, I believe that you have a responsibility to your children first. Pray for wisdom as to how to handle it but you have no reason to fear God if you walk humbly and in light of His direction. If your children are responsive, maybe a conversation with them would be in order but tread lightly as this is their father and they could interpret your actions as the same as his. Typically, the truth if presented in love is the best approach. Sometimes, divorce gets tricky because we try to protect the kids from the ugliness of the emotions and hurt when in fact they see more than they are given credit for. Whatever conversations that you have try to see it from the eyes of your children.