How do I forgive myself for picking a bad dad for my kids?

That's easier said than done. Of course, I can tell you that you didn't intentionally pick a bad father for your children and that you have tried your best to make the best out of the situation you came in. Which I truly believe - I mean, no one picks a bad father (and in extend and in hindsight often a bad boyfriend and/or husband as well). But when those thoughts don't come from yourself but instead are being said to you, they will never replace the current feelings that you're having. So I would suggest to start a journey where you explore what happened and what your part was in all of this in relation to your children. What did you actively do for your children to have missed anything? And when I say actively do, I really mean actively do. You are not responsible for the actions of anyone else, including the father of your kids' actions. Only he is. While I don't know anything about your personal situation; judging from this question, when you take that golden rule into account, I dare to bet that you won't find the things that you've been blaming yourself for. And through this discovery, I hope you'll be able to stop blaming yourself for what happened. Again, I make it sound like it's easy now, but it's absolutely not as they really have to be your own discoveries. And if the guilt is playing large part of your life, you might want to consider asking for (professional) help in this journey.

Firstly, it's beautiful to learn to admit that we make mistakes in life, and we are sincerely never too late to try again, to make amends for a better future. Secondly, though it's so cliché to think that it gets better, we must believe that life gets better, or at least, WE, get better from THE PAST life. Lastly, I would love to wish ye all the best and I hope you will take it one step at a time to make peace with yer soul, for it is so true that you must, 'Never forget the three powerful resources you always have available to you: love, prayer, and forgiveness.' My best wishes & prayers be with ye, stay safe and take care =]