If only things were as simple as some posts in this thread seem to suggest. You need to see a solicitor and get legal advice in order to make sure you get your argument in line first and potentially avoid a problematic situation.
Your DS is already in residence, the title of the house will pass to both of you as tennants in common on the land registry, split 50/50 unless otherwise stipulated.
If your sister refused to move you could go to court for an order for sale, which is normally granted unless your sister made a good argument against.
If she engages a solicitor they would likely be looking to see if there is a case for proprietary estoppel in her favour.
This would require her to demonstrate that a promise was made to her (which can be verbal, not written), that she acted in some way to her detriment, financially or otherwise by living there (ie did she provide care/support during covid) and did she come to rely on that promise.
Its then up to a judge to rule on the case, this may be over-riding the will and granting her the property, or leaving it 50/50 but giving her leave to remain, rent free or at an agreed rent. or of course finding against and making an order for sale.
She is resident in the house, and owns half of it, so any idea of asking her to naff off is naive unless she is not that clued up herself.
You just have to hope that she can be persuaded to do so before talking to a halfway competent solicitor, otherwise its the long haul!!