I think foster care will be a last resort anyway so let's not stress about that right now and focus on the negatives. We don't even know if foster care is going to be required yet. Let's focus on what can be done to keep the OP with her children, help her with her MH, and help them all to enjoy one another's company more.
OP you already sound a bit more hopeful and positive than you did earlier! Just venting to a bunch of strangers can really help. You sound articulate and intelligent so I am sure you haven't irreparably damaged your children by just being too dim to understand how to parent effectively. You have just become overwhelmed and exhausted and can't see a way through. I'd put money on it that you have delayed PND and medication will be a massive help. I was on it for only six months and the difference it made was HUGE and more or less instant.
Then, when you are calmer and less triggered by everything, you can work on your parenting skills and helping your children to manage their behaviour better.
I remember that feeling when I had a baby, a 3 year old and a five year old and they were squabbling, fighting, not doing as they were told, the older two would be bouncing off walls and the baby would be screaming. Some days it feels like I would explode and shatter into a million pieces. I felt like I was losing my mind, and I screamed like a lunatic more often than I like to admit. And I had a supportive DP coming home each evening so it will be doubly hard if you don't have that support.
But here I am 20 odd years later with three big strapping lads, all happy and successful, they all get along, all still love their mum, and honestly they don't remember any of it. I think it was far worse for me than it was for them. This can be you too, one day.
The main thing is not to be afraid to ask for help. I know people dread speaking to SS, it feels like failure and they are terrified. But once you've hit rock bottom you have nothing to lose and they will respect you for admitting you need help to cope. Far better to refer yourself than to wait until someone else is forced to do it for you.
But GP first, and take if from there. Good luck.