Hi XXXXXXXXXXXXXXXX~
Unfortunately older dogs do tend to experience a weakening of the hindquarters with some regularity...it's more obvious in some breeds (such as German Shepherds and Retrievers) than in others, but either way, it's hard to see your pet having trouble and not being able to do much about it.
Now for your questions:
Although I think 1/2 of a low dose aspirin is perfectly okay for your girl (she could actually have a whole one), you might want to talk to your vet about giving her something that lasts a little longer such as Metacam or Tramadol.
It's hard to know if this is simple arthritis or if there is something more going on. Some dogs get spondylosis (which is a narrowing of the spine, which causes pressure on the cord that results in some rear end weakness), and some get osteosarcoma (bone cancer), both of which can present with rear end weakness.
Unfortunately, the only way to know for sure what you're dealing with is through an x-ray of her spine/pelvis area.
It sounds to me like you are a very dedicated parent, but unfortunately aging happens to all of us, and it sounds like this could be what is going on with your girl. I'd ask your vet about switching the meds and then just do what you can to make her comfortable (I see lots of big, fluffy beds and blankets in her future!)
I hope this helps.
Certified Veterinary Technician
Associates Degree in Veterinary Technology. State and Nationally certified.