What an ordeal! I'm so sorry that you and your mother are going through this and it does sound like "home" was the wrong discharge plan. There are a few
ways to go about getting some help and I would suggest that you start down both paths simultaneously to see which one brings help first.
Path #1: If your mother is known to a physician in her community, call him or her a.s.a.p. and ask for assistance. The physician will be able to get the wheels in motion for a) transfer to another nursing home; b) transfer back to the rehab; c) physical rehabilitation at home - however, if you don't feel that rehab at home would help, say so.
Path #2: If you have any contact names from the rehab facility where your mom was before she came home with you, I would call those individuals a.s.a.p. Explain the situation and tell them that this feels to you like an "unsafe discharge" - she had skilled needs prior to the hospital admission and based on the past week, she has skilled needs now which you are not able to manage. Show them that you mean business and keep going up the line until you reach someone who seems to "get it" or better yet, start at the top with the rehab administrator.
If neither of the above pans out and you are concerned for her well-being and safety, I would suggest taking her back to the emergency room. This should be a plan of last resort though because it is the usually the most traumatic option for you both and because hospitals are not meant to be used as a "reset" button. However, falls at any age are a big deal, so for that reason alone it might be necessary.
If you do go with Path #3 and she is readmitted, stand firm and know that your understanding of your mom's needs is much better than anyone's there. Use your voice and tell them the way you see it.
Best of luck.