Not read all post, so apologize if this repeats.
Firstly YANBU
GO for it. You will only get what they consider you to be intitled to. Looking after your DC is full time work IMHO. Benefits are there for exactly the reason you wish to claim them for
As for CSA, you are allowed to opt out of CSA getting involved. AS long as you can tell them you have a voluntary arrangement in place. All you need to do is provide a letter from yourself, and your H stating how much he intends to pay for the upkeep of you DC. To the benefits office. They are happy with this.I have looked into this recently and talked to the job center and benefits agency and the CSA ( about a month ago ) I didn't have to follow this path thankfully as me and DH worked through some things and are ok now, but I wanted to be prepared
You can also register with the CSA, tell them all your details, tell them your H is making voluntary payments. THis is to protect him and you in the future. This means, they wont go after him, and ask him to pay X amount of back dated maintenance for the DC.
I would advise you to do this. A good friend of mine had a perfectly amicable agreement and arrangement with her ex Husband. He paid cash to her, every month. As she had to claim benefits, at some stage the CSA were involved. They ordered him to pay over a years worth of back dated maintenance at the rate that they calculated. Since neither she nor her husband could provide proof of the payments, he had to pay it. She did not get a penny of this money, it went back into the 'system'. totally unfair, and outrageous.
My advise would be,
1 call them, tell them your situation. Let them document that you have a voluntary arrangement. they will contact him and possible his employer, but wont take it any further.
2 Keep records and receipts of all payments he makes to you that you want to be seen and taken into account officially. ( i.e. dont worry about the shopping, or money for DC's clothes etc etc... )
They can tell you the best way to move forward
I'm so sorry you are having to think about this. Its a really sad time, and a really sad phone call to have to make. I didn't appreciate this until a started talking to someone. They were really lovely actually. The woman was so patient and kind to me.
I obviously don't know your circumstances, but like I say, I was really surprised at how just talking to them about our situation, made me feel incredibly emotional. Pick a time when you are feeling particularly strong to make the call.
Best of luck with it all. Take care, and please, don't be feeling bad or worried or anything negative about having to do what you are going to do.