COPD and pets. Any advice?

My mother has chronic COPD on oxygen. I am concerned about her visiting me due to having three cats and a dog. I do vacuum constantly, but you can never get all the pet hairs. Should I be concerned about pet hair and dander with a person who has such a condition. My mother has mentioned about living with me when she can no longer live independently (not sure about that). I could never give up my pets.