Is it permissible to bring a receiver (satellite dish) into the house to fulfill the children's desire to watch children's channels, and the parents' desire to watch news and sports channels, knowing that the questioner has sworn by triple divorce that he will not bring any receiver into his house again? Does divorce occur in this case? And does divorce also occur if the children install receivers in their private apartments within the new house in the future?

Your first question has already been answered. We mentioned that intention is a consideration in an oath. If your intention with your oath was not to allow any channel containing Sharia violations, then you are not permitted to allow the aforementioned children's channels, nor the news and sports channels, due to their inclusion of Sharia violations. If you do allow them, you would be breaking your oath. However, if one of your children introduces any of these channels into their own private home, there is no sin upon you for that, and it does not result in breaking your oath. You are obliged to advise them.