Suffer from extreme waswas because family have a dog

Assalaumalaikum,
I suffer from waswasa in almost every aspect of life, but it is most severe when it comes to purity. My family have a dog and they let it lick them and touch everywhere without washing their hands. They are aware of the prohibition on keeping dogs but they keep it despite that, so it is of no use telling them to get rid of it. We have cats also and the dogs plays with the cats and licks them, leaving saliva on their fur, and cat hair sticks to everything, so it is impossible to avoid the hair completely.

I am afraid of praying with even a single hair on me in case it has saliva on it. I also avoid touching the towels they use to dry their hands after washing because it is likely that the towel collects some saliva left on their arms when it becomes wet. I am afraid that if I stop being vigilant then my prayers will not be accepted because of impurity on my body and clothes. I try to follow the opinion that small amount of impurity is excused but then I feel if I continue ignoring small impurity then overtime the impurity on my clothes will build up until the amount of impurity on my clothes is large. This obsession has ruined my iman and made me feel hopeless. What should I do?