All right,
So if you're Libyan and you would be returned to Libya, it would be extremely unsafe for you children who are Canadian citizens.
You're children would not have access to health care, quality education, and their life would be very unsafe in general.
When you make your H&C applications, you must mention this, you must also specifically mention your children, who are Canadian citizens, would be subjected to an especially exacerbated high degree of risk given their western citizenship.
Despite your reasons for non-compliance, in general Canada tends not to remove people to unstable nations, in your case given children involved, the officer would need to explain why your children's best interest would not be harmed when removed to Libya. So overall I think you have a good chance.
Note: Officers are obligated under the IRPA to consider the best interest of a child in any decision they make.
I would recommend consulting with an immigration attorney who can help you build a strong case.