Thanks for your question.
If you are both named on the registered title to the property then you both have a right to remain there which neither can deny the other until settlement is reached. The Court Order for financial settelement will decide what is to happen to the house and other assets.
If you have young children then their welfare (ie accomodation) will be a primary concern of the Court in the financial settlement you reach. If one party is to have residence of the children then it may be appropriate for the house to be retained in favour of that person and the children.
This can be done by either an outright transfer to the person to remain in the house (but it is unlikely unless that person has the means on their own to pay for all the outgoings on the house (incl. mortgage) and the other person is able to accomodate himself) or a deffered trust of property when the immediate sale is not appropriate (there are various ways of acheiving this).
If you do not work then you may be eligible for legal aid so that you can instruct a solicitor to act on your behalf in your divorce, you can take advice on that and other questions here:-
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