no job is worth making yourself ill, because you do need to be fit to work, to support your family and to have a life.
some how you have to pull back on the work, try to look for ways you can. tell your line management you are burning out because if you don't you will, then you will be signed off sick, and you'll have no choice but to.
This is how I did it. Managament were fully aware of the stress I was under prior to my crash, then I did and was signed off for three months. That's how bad it was.
What would I have done differently in the 6 weeks run up to my crash.
Told my boss, and then seen my GP and explain how I was feeling, book every Wednesday off. why Wednesday? middle of the week, you get the stressful Monday Tuesday over and done with, try to relax on Wednesday and then back Thursday Friday. Be strong and stop doing the work on your days off and evenings. If you have to work in your free time something has gone drastically wrong at work, with resource allocation.
I had to deal with a difficult home situation too, I was constantly getting calls from schools and agencies about mental health & addiction issues at home with OH. I ended up spread thin and I broke.
If home is causing you difficulties and work isn't try to get friends and family to help you, do the same as I said about work, tell them, ask them. Speak with all the agencies you have to such as school let them know what you are facing the welfare teacher and principle should be able to offer help and advice regarding your children.
If your having the difficulties at home try to come up with some way to get out of the house and distract yourself.
Overall your community, friend family work colleagues need to know, then you can ask that network to help you.
Unfortunately. this is all very tough thing to do, but as you are reaching out about burn out, you need to reduce the flame, the only way you can do it is ask for help.
And people will help. You also need to start planning to change or something will break.