The content of cable television is mixed of Halal and Haram. Thus the income from such business would also be a mix of Halal and Haram.
One should try to limit their business only to that which is 100% Halal.
Children who depend on their parents financially are not responsible if the income of parents is not 100% Halal. If the children are independent then they should not rely on the Haram income of their parents.
The business of providing internet connection is not Haram in general. However, if knows specifically about a person who is going to use the internet in Haram ways then providing internet connection to such specific person would be considered assisting in sin.
Your husband should try to provide for you from his Halal income but if provides your necessities from such income that is not 100% Halal then you are not held sinful.
You will not be sinful for staying with your husband in house that is purchased by his father.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America