Is the questioner considered a pimp (dayyūth), and how should he deal with his sister and mother who wear tight clothes and put on makeup, knowing that the mother is regular in prayer unlike the sister?

The "Dayouth" (cuckold) is one who condones evil among his family, and you have not fallen into "Diyathah" (cuckoldry). Continue to advise your mother gently and remind her of the danger of tabarruj (displaying oneself immodestly), for it is a characteristic of the people of Hellfire and a sign of hypocrisy. Make it clear to her that she is responsible for her daughter. If she does not respond, seek help from someone who can influence her, and continue to show her filial piety and pray for her. Advise your sister regarding prayer and explain to her the danger of being lax in it.