Sully wrote up a solid list of
pathologies prohibiting training a few years back.
Doctors are trained with a "risk minimization" mindset, and emergency physicians in particular will always fear the worst case scenario (as they should). However, as discussed at length on these boards in the past, we receive no education in physical training of any sort. This makes it impossible for physicians to perform accurate risk / benefit estimations in these sorts of situations, and they default to focusing on the "risk" side since "heavy barbell training" sounds scary.
Although I obviously cannot give specific advice pertaining to your mother, there is nothing inherently "dangerous" about training with osteoarthritis or rheumatoid arthritis. There is even data to support this for those who insist on seeing published literature for everything.
There is a weight at which the exercises can be performed safely and correctly.