Completely another suddenly abandoned here.
I genuinely don't know if there's another woman or not in your case nor mine, but I do know this:
It really doesn't matter.
The early months are the toughest. Everything is turned upside down, you are bereft, bewildered, hurt and distressed. And yet, you have to keep going somehow for the sake of the children. It is without doubt the toughest time of your life, I imagine.
What I'm also learning is that a disproportional amount of energy, thinking time and, for some, - money is spent on the 'why' (I didn't employ a Private Detective, for example) when in fact you need to spend time, energy and money (if there's any going spare) on you.
If you lack self-esteem and confidence as you say (and given it doesn't sound like he's been that nice and supportive to you, so is it any wonder?), then work on your self-esteem and confidence instead.
So when/if he ever decides to come back, you have the self-esteem to say 'Well, actually, I'm not sure I want you back'.
And if you decided to take him back, you have the confidence to state the terms and conditions he can come back under.
And if he doesn't come back - well a woman with self-esteem and confidence has just come back into the world.
What I've learnt, I suppose, is that I can do all sorts of things that I didn't think I could - and that's helped me get my self-confidence back. But it takes time and it involves being nice to yourself.
Lots of people 'round these parts say 'Fake it til you make it'. They'd be the ones who are right.
Survive and Detach was my bible for coping with abandonment, if you're looking for some reading material.