Praying beside a dog

AsSalamuAlaikum, Sir! My mother has a pet dog and she is very fond of it. When she prays the dog sits besides her and sometimes sniffs or touches her during her prayer! I have warned her a lot regarding this, as I know Angels don't stay in the room or house where a dog is kept. Note: it is not even a guard dog but a pet. Unfortunately, my mother doesn't listen to me, or anybody else, about the Islamic boundaries of keeping a dog! It has been almost two years that she has been praying with the dog sitting just beside her and sleeps keeping it besides her bed. Her statement is, "there is no ayats from Al-Quran or any authentic hadith that says dogs may cause invalidation of prayer or cause impurity." I am very worried about her! Please give me some advice on what I should do or tell her about keeping a dog while praying?