Severe OCD caused by family owning a dog

My family has a dog and 11 cats as pets. I follow the opinion that dog saliva is impure because it is easy to avoid coming into contact with it’s impurity directly, but it also licks the cats, and the cats shed their hair all over the house. With 11 cats, it is impossible to avoid getting their hair on my clothes no matter how cautious I am. I spend a lot of time getting each hair off my clothes and by the time I stand up to pray, I notice a few more hairs have gotten on my clothes. Plus my family members are careless about letting the dog lick their hands and touching everywhere with the saliva on their hands. This has taken away my peace in worship because I am constantly worried that my prayers are invalid because of impure hair sticking to my clothes. Is it permissible for me to follow the weaker opinion that dog saliva is not impure, with regards to the cat hair that may have dog saliva on it sticking to my clothes, towels and prayer mats to avoid this difficulty?