I have not studied the Bible with my kids as of yet because I don't believe it to be from God anymore.
Then teach them that.. they are your children.. not the organisations.
I know it must be an incredibly difficult and complex situation for you to be in right now and I did not mean to lack empathy. I never had a father at all and can see very clearly from the view of the child when one's father is not there to care for you and do the right thing however difficult and hard that may have been for him. Anything less is a form of abandonment. Being true to oneself is always important and even more so as a parent as it will be the substance and foundation of how your children will view you in later years.
Like: "Why if you knew did you let this happen to us".