Oh Tea ((hugs)) no-one is perfect and you are doing a great job. You don't have to make up for their Daddy, you just have to be their Mummy and love them, that's all they need and that doesn't mean being perfect, it just means doing your best and loving them.
Believe me, my Dad was hopeless, absent much of the time and often left me waiting by the window on contact days from dawn till dusk when he didn't show up - it did hurt, obviously, but I knew I was loved and my Mum cared for me and that love was my security blanket. My Mum was no angel either, she has a temper which puts mine firmly in the shadows and I was always the one that caught it (literally) but, I always knew I was loved and being at home with my Mum was my safe place - to be honest my crap Dad didn't figure as long as I knew I had my Mum and my sister.
Everyone has bad days. When I've had a day like that, I go in and kiss them in their sleep and tell them that I love them, then the next morning tell them I'm sorry that I was a shouty Mummy yesterday and suggest we all have a better day today.
Tomorrow is a new day. ((more hugs))
I am just about to buy this book for my boys, to remind them that even though I get cross with them and am shouty sometimes it doesn't change how much they are loved and always will be. I love you stinky face is another good one with a similar message and my boys love it.
Be warned though, I bought Love You Forever a few years back and it makes me cry every time I read it.