Hello and thanks for using Just Answer.
My name is ***** ***** am happy to assist you with your enquiry.
I am afraid that your sister does have the right to apply to the courts for an order for sale under the Trusts of Land and Appointment of Trustees Act in order to claim her rightful half share of the property.The courts have the power to make an order for sale based and from what you have told me, an Order would be made in favour of your sister- she is entitled to her half share, and was indeed entitled to it upon your Mother's death, if it had not been for the Deed of Trust.
Your Mother's Will should really have included a provision allowing you to remain in the property for as long as you wish, if indeed your Mother had wanted this, but as no provision was included, you will have no defence in any proceedings issued by your sister.
As regards ***** ***** can take anything from 4-8 weeks for an Order to be made.
I am sorry this is not the answer you were looking for, but it sets out the legal position.
If you cannot agree then an application to the courts is necessary. You have the right to require her to buy out your share or that the property is sold. If she is living there on her own you have a right to be paid occupation rent to compensate you for her exclusive occupation of the property.