My housekeeper, who is Christian, handles my clothes with unwashed hands, and there is also a dog that makes things impure. My family is careless about cleanliness, making it hard for me to maintain proper purification. What should I do?
Everything is Taahir for you unless and until you definitely know that it has become Najis. Your non Muslim housekeeper handling your cloth with dry hands does not make your cloth Najis.
The dig in your house does not mean that your clothes are Najis as far as you have no evidence that d=the dog touched your clothes with wetness.
Wassalam.