That sounds pretty simple. Just get the solicitor to keep her informed of what's happening (contracts signed, purchase price etc), and send her share of the proceeds to her.
You can transfer the property as personal representative once the will has gone to Probate, so she doesn't need to get involved if she doesn't want to. However, I would get something in writing that she is happy for you to sell the property as personal representative instead of putting it in joint names.