Love of your life after a year?
Oy.

I understand you care for him, but it seems he is not a good fit for your family. Please - you need to care more about your kids' needs and not the BF.

Time to break up OP or make him your underground boyfriend (meaning he no longer interacts with your children).

I also disagree with your decision to introduce him in the first place because it sounds like you knew he was a deadbeat. So now you have proof that this isn't the family man you hoped for so now dump him. New year, new man.

This is not the person you spend your life with. This is your FWB that you hang out with when your kids are with your ex. Not husband material at all.