Got it, thank you.
Sounds like a bit more than spinal arthritis. What you describe is consistent with spinal cord disease, e.g. chronic disc herniation or degenerative myelopathy - the spinal cord is either compressed or inflamed (or both) which causes interruption of signals to/from the rear legs resulting in weakness, incoordination, pain or other symptoms. The inability to defecate normally can be due to different reasons:
1. Weakness/incoordination/pain associated with the condition - physical inability to squat for long enough time for normal defecation to take place.
2. Interruption of nerve signals to the colon/rectum, resulting in dysfunction, enough to make defecation difficult.
3. Intestinal disease unrelated to the current condition (such as intestinal infection, inflammatory bowel disease, intestinal cancer, etc), causing soft stools, which are more difficult to expel; in combination with the weakness, this makes things even more complicated for her.
I would recommend looking into the soft stools to ensure this is not related to a gastrointestinal problem - consider abdominal x-rays, fecal parasite screening, pancreatitis testing (blood test), intestinal function testing (vitamin B12, folate and TLI test). While waiting for results, I would switch food (at least temporarily) to a low fat, easily digestible diet (your vet can recommend a specific one, but I would use either Hill's Prescription Diet i/d or Royal Canin Gastrointestinal) and a course of a probiotic (e.g. Fortiflora) for 10 days. If all is normal, I would continue the diet (as long as it's helping) and add on medication that can help improve pain control and strength; I would consider switching from prednisone to a non-steroidal anti-inflammatory drug (NSAID) such as carprofen or meloxicam (after a 5-7 day "wash out" period - between last dose of prednisone and first dose of NSAID), adding on gabapentin (long term; this drug is used for neuropathic or nerve related pain), a SAMe supplement (e.g. Denamarin) and a omega-3 fatty acid supplement (e.g. Welactin). I would give it 2-3 weeks and re-evaluate; if no improvement, then I would increase the dose of gabapentin and consider adding other pain medications; then if still no improvement after 3-4 weeks, it may be that the mobility of the rear limbs is as good as it gets, unfortunately.
Hope this makes sense and helps. Please let me know if you have other questions.