Please don't say you have failed. You have put your kids first and that take a lot of guts.
Get support. Go to a support group, what you are dealing with is no easy load. Get help for your kids too.

There IS light at the end of the tunnel, it might seem far away, but it is there... stay focus and build a support system for you and your children through a support group, therapy, church or what ever works for you.