I am sorry to hear about your situation.
Assuming you were to put in an application for an order for sale today, I imagine it would be 4 - 6 weeks before the application will be listed. By then of course, it will become clear whether completion is likely to take place on 1 November. Assuming things are still on for the 1, I doubt any Court would grant you an order for sale.
Even if the matter were heard today, the Court would take into account the amount of your debt v the amount of equity in the property. They would place a lot of weight on the fact that it could potentially leave your client homeless when there is a buyer lined up. On the the other hand, had there been no buyer, the Ct would look as your interests as a creditor with more weight.
I am not sure as to the buyer's position - is she paying in cash? If they are in fact ready to proceed, you could threaten them with enforcement proceedings (which could incur more costs) and also explain that you are charging interest at 8% - in which case she could lose the �10k she is seeking to protect by delay.
As to your position, you would effectively be selling the house qua trustee. As such you owe a duty to the "beneficiaries" - ie the other chargees, and the equity holder. In that situation, you should attempt to ensure the best price. We all know that mortgage lenders don't - unfortunately, many people are not in the position of being able to pursue them for badly selling their property.
The alternative is to suggest to the daughter that instead of buying the property, she just settles the charge - then you will go away and she will have a charge on the property.