Unless she paid you half the market rent, you could apply to the Court for an order. You could either ask for an order that she pay you half the market rent or an order for sale. She has no automatic right to live there - since were she to live there, she is getting an unequal benefit from the estate. I would suggest that if she can't afford to pay the market rent, you either sell the property or you defer the rent so that the rent is paid to you out of her proceeds of sale. However, this would need to be done properly to avoid problems down the line.
If I can also correct a common misunderstanding. "Going to Probate" is something that most estates will need to do - it is not dependent on there being a Will. It is dependent on the value of the estate. Only small value estates or cases where the only asset is a property which is inherited by the surviving joint tenant(s) won't need a Grant.
You get a Grant of Probate where there is a will with executors; you get a Grant of Letters of Administration with Will Annexed where there is a Will but no executors; you get a Grant of Letters of Administration if there is no Will. Generically these are known as Grants of Representation; colloquially they are know as "going to Probate".
If there is no Will, the estate will fall to be distributed under the intestacy provisions - which if the closest relatives are Noth and his sibling, means that they would inherit the house. It is automatic in the sense that this is prescribed by the Administration of Estates Act 1925.