Well, first of all, sorry if my english is not too good, it's not my mother language.
I get you, I also struggle with those kind of thoughts and it's not pretty.
I'm a mom too and let me tell you one thing: Our kids do not judge us in any way, as they are children and they don't have that sort of thoughts, so you should stop feeling guilty about it.
We live in a rotting society, out nature is falling apart, so I think it's normal for a sensible being to feel like there's no point in living anymore, and of course I've been feeling it for long time now, it just comes and goes.
I tend to cry for hours, just thinking negative shit about myself, blaming me for so much, until I fall asleep and then I wake up and feel a little bit different.
I'm not really sure how I can get rid of these sensations, this emptiness, lack of sense in living, so yes, we have to learn to embrace it, it is a part of us after all, it's our dark side, and it's okay. It's just a proof of our greatness! We are so wonderful that we have this other part of ourselves, like a monster sucking our energy and telling us we are not worthy... I think we are worthy.
Life is love! Hate is not the opposite of love, FEAR is, that's why we constantly feel like this, it's our lack of love... Well, like Bjork says, all is full of love, we just have to learn to notice it, and even if we're feeling hopeless, there it is. Just look at the trees, growing apples, animals feeding their babies... That's love.
Hold on to your beautiful child and learn to love yourself, just as I am.
You're not alone.