I'm no expert but I'm going through something similar so I thought it might help to let you know what I'm doing. I don't have children and as much on my plate as you.
Like you, I have been depressed for some time now and many things have worsened this, an awful diagnosis in my family and then the death of my Father a year ago to name the worst. As my Dad died I had left a job and started a new one so I had to "bank" my grief and throw myself into the job. It was the wrong job for me, they pushed me into basically pretending to be qualified while they trained me, but never trained me so I've been drowning for almost a year. Things have slipped at work and home and I have been deeply unhappy. The year anniversary of my Dad dying has really heightened things for me, not so much that he has gone, but the circumstances and the aftermath I had to deal with alone was very distressing.
I went to the DRs in October and was put on Sertraline and that was working well but this month I had a breakdown and just could not cope. The doctor has upped my dose and signed me off work for a month.
My DP urged me to quit my job, as did my Mum and my friends having seen how miserable it has made me. Fortunately we can survive on DPs salary for a few months. I have handed my notice in and as I'm on sick leave, do not have to go back.
It's been a huge relief. I'm going to take a month to look after myself. I'm getting counselling, seeing a dietician (part of my problems manifest themselves in eating) and generally looking after myself- reading, exercising, sleeping. I'm not under any illusion that this is a cure but the weight is already lifting. I'm also keeping to a structured routine because I know I could all too easily hide under my duvet all day.
If I was you, I would probably leave my job. You are unhappy there and you can manage financially without it. You need time to care for your brother and be there for your kids, but ultimately you need time for you too. Anyone dealing with what you are would be under immense pressure without depression and anxiety thrown in, there is just no way one person can cope. What reason would you have for keeping the job? Maybe you could speak to your doctor and ask to be signed off for a while longer so you can make the decision? Even if you do quit, it doesn't have to mean you stay at home forever. You might eventually find a job which is less demanding and means you can balance your family too. But you're in a fortunate financial situation and I think you should use it to your advantage.
The other thing i have done is TALK. I'm renowned for being a stubborn stiff upper lip sort, I am more than happy to listen to and support my friends with problems but cannot stand to talk about my own. But my DP urged me to tell me close group of friends and they've been brilliant (and they knew all along really so I was only kidding myself that I was keeping my head above the water!). I've also started to be able to say "I'm having a bad day today" to DP and that's really helped us both because before I would just withdraw which was tricky for him.
About your Mum and ICU. Please don't be angry at yourself. You were at work, but you could have been anywhere; watching a school play, in the supermarket, in the bath, asleep. These things do happen and its awful but you did get to be with her, I hope you can in time cling to that memory and not the distress. I'm sure she would hate you to beat yourself up over it.
I feel like i've typed loads and made it all about me, but I wanted you to know you're not alone and give you my own experience because I feel like I'm making the right steps for me.
Oh, and finally. Would you consider going back on ADs for a little while? I'm normally a bit anti them in the way that some Drs seem to put people on them very easily but I've found they have balanced me out enough to let me make sense of everything and start making a plan to "rebuild".
Thinking of you. 