Thanks for your question.
I would firstly advise mediation between you and your partner. A family mediator can help you to agree on arrangements in a professional manner with legal advise from trained experts. Please have a look at https://www.familymediationcouncil.org.uk/ to find a local mediator. The reason I mention this is to make the process easier and less stressful for both of you. It works well and it saves you going to court. Lastly, since you have children, it is important to disrupt them as little as possible and co-operation can help to maintain a stronger family relationship in the future.
If mediation does not progress you should then proceed with an application to court under Form A for financial relief once the divorce petition has been issued.
As mentioned above, family mediation can help you to agree on child arrangements. If you come to an agreement on certain issues such as where the child will live, child maintenance and so on, this will be legally binding with the solicitor and save you going to court hearings.
If children are involved, one of the main considerations will be to disrupt the child as little as possible - the child requires a "family home" with each parent. This means it is critical a second home can be bought for the other spouse if necessary. Both parties need to be housed appropriately.
The fact that the house is in your name doesn't actually have bearing on who gets the house.
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. For your information the criteria considered by the court in these matters 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.