She's definitely exceeding expectations for lifespan for a dalmation, so I it's hard to see them getting weak this way when mentally they are still with us. I would speak to your vet about adequan, which is an excellent medication for things like joint pains, arthritis, and weakness from bone due to age. Not only does it help cover pain and lubricate, like anti-inflammatory meds with glucosamine supplements as well, but actually helps to heal, and in a few weeks, significant differences are seen. It really is a wonder drug, with barely any side effects, again unlike things like prednisone, which is another option if needed.
Here is a link to adequan, it is given as injection, which your vet can get for you and show you how to administer or can be done at the office:
I would cut back on the exercise for now as well, as it may be too much for her at this time. While it's good to get them up and moving, once arthritis is really set in, it can cause more pain to be too active. Other options for her include the non-steroidal anti-inflammatory meds for pain, or acupuncture treatments, which I have also personally seen make a huge difference in back end weakness. You can find the ne closest to you from this link:
Best of luck. Let me know if I can help further.