A.R.
He absolutely does not get another chance.
If you stay in this situation, you are not "staying together for the kids". You are staying there letting your young boys that it is okay for mommy to be hurt, it is okay for women to be subservient, and it is okay for them to be violent.
You mention you have a huge support system in your family. Run, run, run to them and get their help.
Get away from this man ASAP. Being an alcoholic and bipolar are excuses. Many times men will say they do it because they "can't control their anger". If this were true, they'd beat their domestic partners in public and in plain view of other adults and not wait like a coward until they are in the privacy of their own home or hit in places where the bruising can't be seen.
It is better for your children to say they "came" from a broken home than to continue to live in a broken home.
If you can't do it for yourself, do it for your children. Abuse in any form is a dealbreaker.