I am a father not a mum so I hope that it is okay that I answer this.
Babybump: Your relative is right to be worried. A mortgage can only be given based on income. If the income your friend will have isn't sufficient then she won't get a mortgage no matter how big the size of her deposit. Also, even if your friend moved into employment straight away a mortgage lender is likely to require some history of employment earnings - maybe six months, maybe a year, maybe longer.
Rionne noted that your relative could apply for the right to stay in the family home. That is possible and can be granted but: (i) from what you write it seems that the divorce settlement already provides for a sale; and (ii) in many if not most cases a sale is preferable to getting a court order for a right to reside in the family home.
Be careful re shared ownership property. Some of the issues that can come up are described in this article in the Independent:
http://www.independent.co.uk/property/h ... 05884.html