I am sorry to hear about Snow's problems. My name is Rebecca. I am a veterinarian and will do my best to help.
Since I can't see and examine her, some additional information will help me to give you the best answer.
How long ago was she injured? Is she using the litter box to urinate; is it just feces she leaves around the house?
Is she walking normally now, on all four legs?
Was an Xray taken of her back when she was injured?
It sounds like she has a spinal injury, that may have caused damage to the nerves of her colon. She may not know she has to defecate, and so the feces just passes wherever she is. This kind of spinal injury can get better with time, but sometimes it does not. It is a good sign that she is showing signs of recovery by eating and moving better, so she might just need more time; nerves heal very slowly. There are medications that might help, such as prednisolone, if this is nerve injury.
Let me know a little more about her, and what other questions I can answer.