Lissa,
Have you started divorce proceedings? If you have, you could apply for 'Maintenance Pnding Suit' which is a court order for interimm maintnance from your husband. Have you got the CSA involved in the case at all? He should be paying 20% of his nett income (after Tax and NI and pension) in child maintenance for the children.
As to him co-habiting, it weakens his case for his housing needs. He is sharing with his new girlfriend, so his housing needs are less than if he were living alone.
If he is on the mortgage and deeds, he still has a financial interest in the house and that would need to be settled by mediation or through court if no agreement could be found.
Are you claiming all the benefits that you can? Like Tax credits, council tax benefit and child benefit? You can check online at
www.entitledto.comCheck if you are entitled to Legal Aid -
http://www.communitylegaladvice.org.uk/en/legalaid/Hope it helps
Mike