I'm going to speak plainly. Partly because I'm worried about the language you shout at daughter and the language you use to describe your children. And partly because I will never forget the harsh (but ultimately fair) words of a psychiatrist after I'd made a suicide attempt years ago.
I can only imagine how hard it is for you to be both depressed and have to cope with two children without support from your husband. But you stand at a crossroads. You can either get help right now - practical help for the children and psychological help for yourself -- or you can continue to catastrophize (I use that term with some reservations, but it's what I did when depressed) and lash out at those vulnerable children and cause real, lifelong damage. Imagine in 25 years reading something on here or elsewhere about a daughter coming to terms with a mother who resented her, screamed at her and blamed her for her stunted life.
I suspect you really want to scream to your husband, but he's practically (and most probably, gratefully) absented himself.
More about him. Alarm bells ring that a father who has been away all week chooses (yes, sorry, 'chooses' - it IS a choice) to spend the weekend on the laptop. Even if you weren't depressed and harried and can't even find time to shower (is this true? Can you not put on Tom and Jerry for five minutes and get all of them in the shower or bath with you?) it would be neglectful. It is not good parenting. If things have 'blown up' (and don't they always) then he has to time manage. Do the work when they are in bed and simply get less sleep. But no, he probably wants to avoid you and the children. Strange, seeing as he wanted them in the first place. My apologies if I've read the situation wrong, but that's what strikes me.
If he can't time manage, if he has no time for the children or you, then he should have serious thinking to do about his career and what he wants from life. In some ways some men can be much more insecure than women, who after all, if they have children, have to career change -- at least for a while. Some men, particularly those driven types in high-pressure, highly paid jobs simply couldn't countenance just 'being' without the accoutrements of power and prestige.
But you never ever go to your deathbed glad that you worked 30 more hours a week to earn 50k more (or 500k more for that matter). You are never glad that you never really spent time with your family (instead wax lyrical about them to colleagues and drive them to boarding school once a week at best) to underwrite loans or help Company A take over Company B.
It is an arrid existence but we can easily get locked into it. Your fixed costs rise, school fees starting piling up and before you know it, 500k a year is 'scrubbing by'. What it takes sometimes to earn that 500k isn't worth it for some families. It's why I left.
It is unlikely he'd consider a career change or a sabbatical, but you've got nothing to lose bringing it up.
Now you. You need professional psychological help. Possibly medication. I think you could also benefit from a meeting with a child psychologist, or family psychologist (in fact, you could all go) to help attachment issues.
Immediately, you need to relinquish your ideas about being the perfect SAHM and get some childcare -- one full day or two half days perhaps.
And you need to find a way into your daughter's mind. Treat it as a project (seeing as you are a high achieving sort). Get books (Playful Parenting by Cohen, How to Speak etc and some proper psychologist stuff) and make yourself play with no interruptions with her, following her lead. You won't feel like it, but make yourself do it. It can't be worse than the shouting and screaming, can it?
Please let us know what you decide.