Is the questioner considered sinful if her household members use the internet modem, for which she pays monthly, to watch TV series and movies, despite her warning them, and their failure to respond to that?

It is not permissible to watch films and TV series that include auditory or visual prohibitions, and whoever assists in this commits a sin. It is necessary to prevent family members from watching forbidden content, and it is preferable to convince them to use technology for beneficial purposes and avoid disobedience. If they do not respond, a means of prevention must be adopted, such as using a password to prevent internet access.