Mo, I think you are absolutely right about his mum, not worth it, and your dcs need a good relationship with their GPs. I don't think he will focus on CMS until he has a court order if left to himself. . I think he is deluding himself. As well as being a control freak I think he doesn't believe anyone about money unless he has agreed it himself.
In my organisation you would need to contact the head of HR, cc the line manager, and him preferably so you can say you have been completely open, with a copy if the CMS calculation and proof that he is the father. If you had been married it would be proof of separation . And you may need that now, so some emails might help. You might need on ask them what further proof is required. , if any. ( As this will scupper his reputation in one level, it would be fair to let him know this is what is going to happen. ) We would then put it to our payroll operator, which might take a month or so but for us, if done by the tenth of the month should be actioned.it will depend what proof they need. I've never had to authorise a back payment, but by agreement I think it either comes out over time of the monthly salary, or is paid off out of personal savings.
Hope helpful. Keep cheerful...