Although I can only claim for 2 dc we were housed in a 3 bed but housing benefit cap at 2 bed rate as 3dc doesn't exist in their eyes, I use a lot of benefit to cover shortfall I need to keep the house I can't lose it.
I suspect you are "benefit capped", as families with 3 children often are. The cap reduces total benefit income to £384.62 pw (more in London), and comes off housing benefit.
You should still be entitled to full child tax credit for all 3, plus whatever benefit you get for yourself, as long as you are getting child benefit for all 3 children. (If you're not, because someone else is getting the CB for one of them, this can be sorted, too. PM me if you want to know how to go about it).
If you were working for 50 weeks out of the year before you started claiming, you have a "grace period" of 39 weeks before the benefit cap is applied. This also applies if your ex was working for that period, even though you have now split up.
If you get PIP or any of the kids get DLA middle or higher rate care, the benefit cap should not apply.
Even if the "grace period"/PIP/DLA doesn't apply, then contact the council, explain your situation and ask for the form for a Discretionary Housing Payment. These are for families who are struggling because of the benefit cap or bedroom tax and, if your application is successful, could cover the whole shortfall between your rent and your housing benefit.
And if you have debts that you are struggling with, please get in touch with CAB, Christians Against Poverty or Step Change and get specialist advice. They are very helpful, and won't judge or preach!
It's disgraceful that people are put in such dreadful situations as yours, especially when they've already plainly been through a very tough time. It makes my blood boil.