Your mother died intestate with no spouse and hence the proceeds of her estate are divided equally between children.
You are going to need Probate Letters of Administration to deal with the estate and the sale of the house.
If your brother and sister refuse to agree to the sale of the house you can apply to court for an order for sale to make them sell it and you can ask the court to award the legal costs in respect of the application against them.
It is most unlikely that any defence they have to your application would succeed.
Meanwhile, if anyone is living in the house, you are entitled to one third of a market rent.
The fact that your sister may say it was the family house and it has memories is irrelevant. If there are no dependent children, it is also irrelevant where they are going to live.
If your brother has children under aged 18, the local authority will provide alternative accommodation but not until there is a court order.
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