Say for example a halalachly uneducated Jew intermarries and then years later realizes the marriage is a Torah violation and has great regret, yet he loves his wife and there are children involved. He cannot ever bring himself to leave his family.
Can this Jew receive forgiveness even though he has no intention of ending the marriage? Can he seek and receive atonement on Yom Kippur for something he feels he cannot change or is that just denial and hypocrisy?