CMS maintenance calculator and ask him for the money.
https://www.gov.uk/calculate-child-maintenance
If he isn't amicable CMS claim ASAP. Is he self-employed or employed? The former and abusive thrown in - she should expect him to be difficult.
Employed is much easier - CMS take it from his wages if he doesn't pay.
Re house, if she has looked after children and reduced her career, she will get more than 50% in selling up. Plus pensions are shared too and all assets. Practically, get the mortgage on interest free if possible to reduce overheads. Claim benefits including child benefit as a single parent and also universal credits. None are back-dated. Do it today.
Practically, file for divorce if she has any written admission from him about the affair then file on grounds of adultery and tell him he is liable for the court fees.
If not, unreasonable behaviour and state something non- combative. It's not worth the fight. Share the court fees.
I believe you need a MIAM report now to proceed (mediation). They only need to attend one session together and agree to divorce and it should be signed off to proceed to court. There is a time limit on them. Getting to decree nisi is step one and then it doesn't matter how long it takes until you get to the final absolute.
Look for a Facebook group on DIY divorce so you know how far she can get without a solicitor. They love making money by sending stupid letters. Practically, this is not necessary.
Emotionally she must completely disengage with him. This will be the hardest hurdle. thanks