Equity has everything to do with it. The reason a bank will "normally" consider a short sale is because they think they will be better off (and most times they are) taking less then they are owed then taking the house back (Foreclosure or Deed in lieu) and then having to sell it. In your case the bank should have no problem auctioning or other wise selling the property and getting back what they are owed. Now if the property was worth say $275 and the mortgage was $250 they might still take a small loss and sell it for slightly lees then owned (Say $240) because when you add on the foreclosure costs and the re-marketing cost they might still come out ahead or at lest even and it would be done now not later.
Assuming you try to work the short sale (by the way if you are not good with details and negotiating don't bother because SS have a lot of details, negotiating, paperwork and follow up) the bank is going to want to get a BPO or an appraisal and if that comes in at anything close to $350 I think your deal is dead.
In regard to your statement can they force here to refi? No they cannot but the can definitely foreclose on her for defaulting on the loan. Now maybe I miss something somewhere but that is how I see it.
Let me know I can be of any help (I guess I have not been much so far)
As I said before Good luck.
Jay