CAN I FILE IN AZ? mother relocated to AZ; medical mistake occurred in IL while she was resident there

It looks like punitive damages are allowed in AZ and schedule of payments is not??? My mother, 87 y/o lives in Tucson. One year ago she was subject to medical mistakes in suburbs of Chicago, IL - - would she be allowed to bring suit in AZ or do I have to bring suit in IL? (Older Adult Healthcare specialist physician did not return my call, had a nurse tell me not to bring my mother in to the office because her symptoms sounded like a flu going around last fall/winter 2012 which could last for a few weeks. (My mother was diagnosed with diverticulitis by the doctor months PRIOR to the call and treated with antibiotics) After about 10 days - - I called on a Sunday night as I was concerned and the "on call" physician of the group told me to rush her to the emergency room - - she should have been seen since her file indicated she had diverticulitis. Upon arrival she was put in the ICU in grave condition since she had been suffering from a ruptured bowel which over time had formed a large leaking cystic sack which caused her pain- - she was in sepsis. Several procedures and an Illiostomy resulted with other goof ups during the stay sending her back to ICU with kidney failure as they allowed her to dehydrate after her illiostomy. finally my mother is coming around, but she does have some dementia and there was a great deal of unnecessary pain, suffering, time and cost incurred as a result of their mishandling.