OP, I think you need to consider whether the children being resident with you is what you want, for your own sake, or because it is what is best and safest for them? You really, really need to examine your motivations here, I think. Do what is best and safest for them, not what makes you happiest.
Can you honestly say you will never get so drunk they are unsafe again? I don’t think you can, hand on heart, in all honesty. I’m sure you think right now “I’ll never do it again”, but I bet if you asked yourself before the most recent incident if you would you did, I’d bet that you would have said “absolutely not”. If you think that 100% there is “no chance”, I would tell you that you are lying to yourself, as much as you are lying anyone else.
I say this as the family member of an addict, who has wreaked havoc on his ex-wife and children. He is not a monster, he has many positive points- articulate, intelligent, interesting, funny, kind and generous. When sober, he is genuinely a lovely man. Drunk, he is an aggressive, sharp-tongued horror. Tipsy he is sarcastic and cutting, can be quite cruel, and easily angered/brought to tears. I know, without a doubt, that he loves both her and his children. That has never been in doubt, he desperately did not want his marriage to fall apart and not being able to see his children every day was a huge source of pain and sorrow.
The issue is that his addiction/illness had a greater hold on him for a long time and, in the end, his addiction was stronger than his desire to get better and stay better when it mattered. Sadly, the damage he has done cannot be undone. He has lost his wife, his home, and sacrificed his children’s stable childhoods. He has very fraught relationships with his children, who harbour so much pain and resentment towards him (with good cause). He lost his career and he has chronic liver disease, amongst other things.
I think if he had stepped away (I’m not saying no contact), sought proper help, and taken the time to get better, he might have had a marriage and a family to go back to. He might not have damaged his children. He might have a career and a healthy body. It’s too late for him, and his family, but it’s not too late for you. If you take the hard decisions now, put your children and their well-being first, you will be giving you all the best chance of a happy outcome.
I understand that you don’t want to be separated from your children- but I imagine their father doesn’t either. I can only imagine the worry he would have if he were to leave you alone with them. I don’t mean to upset you, but you are quite casually dismissive of his views of “one drink being one drink too many”. For you, it is. You have shown you only managed a matter of weeks before relapsing. Not a “blip”- don’t minimise the seriousness of this. This relapse came at a time when you knew you were under intense scrutiny by the courts regarding your abstinence from alcohol- you had a falling out with your friend and got so drunk your children were unsafe with you. What will happen the next time you are upset or angry or stressed? You have shown him that there is a chance your shared children will be endangered by you again- it’s too soon to say you won’t do it again. If you couldn’t do it with this court supervision hanging over you, I think it’s wishful thinking to believe that it could never happen again.
I’m glad you are seeking help, and it’s a good first step, but you aren’t in recovery yet.