Hi smiffy
As you said : a right mess.
Now let's see what can be cleared and tidies up.....
One thing that your husband must pay, no ifs, no buts, and that is
child maintenance.
Go onto the CSA website and look at their calculator.
You do not say whether you work, but with three very young chidren I suspect you are not.
The next thing on your 'to do' list is to contact your council via the Jobcentre plus which are now in charge of benefits. You make an appointment and tell them of the situation, because if you have no savings, you are entitled to various benefits : child benefit obviously, child tax credit, income support etc.
I know that the last thing on your mind at present is filling in forms, but it has to be done.
You mention that you want to divorce him for adultery. That is fine. I just want you to be aware that it may be of great moral importance to you, but when it comes to the division of your assets, it is not taken into account in any way WHATSOEVER.
You will probably rail at the unfairness of this, but that is the law. The earlier you know, the better it is : you will NOT get more because your husband has committed adultery = the reason you may (and probably will) get more than 50% is because you are the childrens' primary carer and the court is first and foremost interested in their wellbeing.
As for the mortgage : are both of your names down as being responsible for the mortgage ? If the answer is yes, it means that the mortgage lender is not interested in who has stopped payments - they want their money. Period.
What you can do temporarily is talk to the mortgage company, explain the situation to them and take a mortgage holiday.
This also needs to be done asap as mortgage lenders get nervous after a couple of months default on the payments.
If your husband alone is responsible for the payments, there could be serious problems ahead for you.
I am sorry that this post is not more optimistic, but it is better to know the facts, however unpalatable they may be.
Good luck
Red XX