Hello, thanks for your question.
My name is Tony, I can assist you with this.
Were you married?
Okay. Then yes, you could seek to force the issue.
You can apply to the court for an order for sale which should force her to settle the dispute by buying you out.
She is obviously not entitled to your property at your expense.
Yes. Having to care for children is not an answer to acquiring somebody's interest in property! However, what order the court makes will take into account the fact that there are children there. Relevant issues will be whether, for example, they are at a local school and being forced to move at a specific time will cause too much disruption.
Under the Childrens Act, the wife could apply for property adjustment orders, which means she would get the right to reside there, but the court would be able to make an order to compensate you in terms of the interest you lose by forcing her to make payment to you.
I can understand your feeling about this! I would suggest you get a solicitor to write her a letter inviting her to formally buy you out, and if not, then you start court proceedings with a view to forcing that to happen.