One more thing.
Your solicitor is correct about 20% of your earnings - but this is after tax, NI and PENSION CONTRIBUTIONS. Therefore, if you want to reduce the amount you pay set up a pension scheme, if you don't already have one, and put as much as you can in there each month. I'm not sure if there is a maximum amount you can pay in.
Use this site as a rough guide to how much you'd have to pay. Having the children for a night or two each week will help reduce the figure further, and would be fantastic for you and them.
https://www.gov.uk/calculate-your-child-maintenance
Being self-employed helps a lot too. The CSA hate dealing with self-employment cases.