Honestly? I can only speak on the money side as my ex thankfully wasn't abusive, so sorry you went through/are going through that
I never included that money in my budget.
I was much less well informed and experienced in dealings with both ex and govt when I first split from mine. At least you have mn to hopefully see you straight!
2.5 years he sat on the forms from csa (as was) until someone I met who was also a single parent (father with care in his case actually so to pp who wondered if women can be just as shit - yes!) who advised me to contact my Mp. At this point I had no idea mps could deal with stuff like this - I know much better now and probably bug the life out of current Mp 
This lit a fire under csa who lit a fire under ex FINALLY
But he still played the system which resulted in dd and I being doubly "stung" because at this point I was on income support Etc and Cm was included for benefits calculations then. So when I DID get a payment I was no better off and if I DIDN'T or he UNDER paid for the first few months dwp assumed he WAS paying and in full and deducted from my benefits.
Thankfully that's since been changed.
My ex was army too so it's not like the govt didn't know EXACTLY where he was and EXACTLY how much he was paid cos they employed him! However, the army can be very obstructive on this matter and very much drag their heels.
Eventually a deduction from earnings order was obtained and enforced, only for ex to get himself kicked out the army!
He then went into a "self employed" situation, lied to me he wasn't working at all but stupidly posted a work promotion on his Sm! (Yes he's not the brightest!)
So I contacted (then) cms and reported this who told me they couldn't do anything on the basis of a sm post...but the person whispered to me that Hmrc COULD look into whether he was declaring his earnings honestly and that i might want to contact them to report possible tax fraud!
Cms can then get the info from hmrc and proceed accordingly - which they did.
But the whole of dds childhood he never paid regularly or always the full amount, I calculated what he "owed" at one point and it's into £10,000's in my case - more from the length of time than him being a particularly high earner.
In your case your main priority has to be your and dds safety of course, but if you can do so safely then I would advise contacting both your Mp and hmrc. Mps have to legally respond and act within certain time frames for constituents. This is regardless of their opinions or party affiliations on the subject you're contacting them about. My Mp at that time was a Tory who vehemently disagreed with csa etc yet absolutely went to bat for the current laws to be enforced.
Hmrc also have obligations to investigate reports of potential fraud.
If you need advice on budgeting which is also something I'm now much better at than I once was out of necessity. You could post on this thread or a new thread and myself and many others would be more than happy to help and advise. You can even pm me if you wish?
So glad you got out that's amazing!
Wishing you and your Dd the very best for your new future 