Maintenance for 2 kids from a musician

Hi everyone,
I would like to ask you please for advice.
I am a mother of 2 kids, living on a lone parent payment.
My ex-partner is a self-employed musician.

We are separated for 5 years now and I have tried to have a verbal agreement regarding the maintenance for our kids, rather then going to court.
However, now that the kids started going to school and my payments have been reduced to bare minimum, I am really finding myself struggling.
I am getting a maintenance of 400 euro a month (50 euro a week per child).
However that always gets used on some bills, and during the winter times on oil and coal. I cannot get a full-time work, cause I wouldn't be able to afford a childcare and don't have a family to help out, plus I have health problems with my immune system, so am on a treatment. He is always out doing gigs, rehearsals etc. and moaning he has no money.
However, he lives in his mothers house and he spends his nights drinking.

I am having social workers now helping out a little bit and was told to go to free mediator to get the maintenance sorted.
I am really scared, because how can I prove them he has an income, when 90 % of his income is paid by cash?
He will sit there and will complain he is broke (and i know it's not true)

I am not asking for any huge amount, but I think 500 month would give me a bit of relief.
Or for how much should I be asking him for?

Any thoughts, please?

oh, I should ad that he is getting 100 euro a week from social welfare, which is exactly the money he is paying us, so he just hands them over to me. However, he refuses to ad a little more from his own pocket.

I know a few musicians like that and it is as you say. Sickening really. The dole is their pocketmoney and they pick up enough playing gigs. I think it would be very, very hard to prove income. You might need a PI to take note of all the gigs he plays over a few months and try use an industry person to calculate the expected pay.