A cash offer is always better than an offer that requires financing, however as the seller you can not be forced to sign any offer. If your mothers offer was first you should have only signed one offer and that have been submitted to the bank for approval without a wait. The cash offer could be a back up offer and not submitted if you already signed one offer. you can not sell the house to two different people, so you should not be signing more than 1 offer. Most banks can only look at 1 offer at a time anyway, you still own the house, the bank simply decides if they will reduce what you owe to allow you to sell it.
please see my blog for more tips on getting a short sale approved.
Is there any chance the other buyer is buying this as an investment and will let you continue to rent? If not, maybe you're meant for something better.
Best of luck!