Firstly, if you remain the main carer for the children you can pursue an application for child maintenance from him. This can be done through the child maintenance service (http://www.cmoptions.org/en/other-arrangements/statutory-service.asp) - they will do an assessment and advise what the legal obligation for him is. They will then advise you of options to collect payment from him.
In relation to the divorce, this can be pursued under either the grounds of unreasonable behaviour or adultery - depending on the facts. Once the petition is issued you can consider pursuing an application for financial relief which will consider both your financial positions and assets, and both you needs and the children's needs.
You should also be aware that despite the matrimonial home being in your sole name, as you have lived in it as husband and wife he will have matrimonial home rights - so he will have a right to live in the property until divorce or a court order excluding him from the property.
In relation to the financial matter initially this should be attempted through mediation - you can find independent mediators here: http://www.familymediationcouncil.org.uk If a settlement is agreed this can be submitted to court under a consent order (together with a D81 form outlining your respective financial positions).
If mediation does not progress you should then proceed with an application to court under Form A for financial relief.
You will both need to provide each other with full and frank financial and income disclosure, as well as disclosure of your reasonable needs. The Court's starting point is a 50-50 split of all matrimonial assets and ensuring that both your needs are met in relation to both assets and income. The criteria considered is:
1. The income, earning capacity, property and other financial resources which each of the parties to the marriage has or is likely to have in the foreseeable future, including in the case of earning capacity any increase in that capacity which it would in the opinion of the court be reasonable to expect a party to the marriage to take steps to acquire;
2. The financial needs, obligations and responsibilities which each of the parties to the marriage has or is likely to have in the foreseeable future;
3. The standard of living enjoyed by the family before the breakdown of the marriage;
4. The age of each party to the marriage and the duration of the marriage;
5. Any physical or mental disability of either of the parties to the marriage;
6. The contributions which each of the parties has made or is likely in the foreseeable future to make to the welfare of the family, including any contribution by looking after the home or caring for the family;
7. The conduct of each of the parties, if that conduct is such that it would in the opinion of the court be inequitable to disregard it;
8. In the case of proceedings for divorce or nullity of marriage, the value to each of the parties to the marriage of any benefit which, by reason of the dissolution or annulment of the marriage, that party will lose the chance of acquiring.
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