Would it be considered an ongoing sin upon the deceased if his children were to open movie channels after his death, even though he forbade that during his lifetime and disavowed anyone who would do so after his death?

It is by the grace and mercy of Allah Almighty that He does not recompense a person except for what they earn, so no one bears the burden of another, as Allah Almighty says: "And every soul earns not but against itself, and no bearer of burdens will bear the burden of another" and His saying: "Whoever is guided is only guided for [the benefit of] his soul. And whoever errs only errs against it. And no bearer of burdens will bear the burden of another."

As Al-Sa'di (may Allah have mercy on him) said: The guidance and misguidance of each person is for themselves. No one bears the sin of another, nor does one ward off from another an atom's weight of evil. And Allah Almighty said: "And no bearer of burdens will bear the burden of another. And if a heavily laden soul calls [another] to [carry some of] its burden, nothing of it will be carried, even if he should be a close relative." So, on the Day of Resurrection, everyone will be recompensed for their deeds, and no one will bear the sin of another.

Thus, a servant is bound by their deeds, and the misguidance of others does not harm them. Allah Almighty said: "Every man, for what he has earned, is pledged," and "Every soul, for what it has earned, is pledged." And He Almighty said: "O you who have believed, take care of yourselves. No harm will come to you from those who have gone astray when you have been guided."

Therefore, the honorable father bears no sin for his sons' actions, because he disavowed, while still alive, the use of what he purchased in ways that displease Allah, and he did not permit its use during his lifetime except for good. This device—the satellite dish—is subject to the same ruling as wealth that the sons inherited and used in ways that displease Allah Almighty.