BS”D
The famous letter of 1979 tried and succeeded in making OWNING a TV into a “wedge” issue between followers of Rav Yoshe Ber and followers of the Agudah Roshei Yeshiva (The poskim of the time (such as Rav Moshe, Rav Yaakov & Rav Ruderman) did not sign it, IIRC). This is one of the main reasons why the “Yeshiva World” is so against TV, Lehavdil Ben’nenu Ubain “Ha’Amim” (sic).
It has been said many times by the rabbonim that if they could Assur Internet they would (and they tried, at first), probably for the same reason, to make it a “wedge” issue. When they saw no one (working) would listen, they changed their minds to what the Tzibbur thought was doable (as per the concept of “Gezairah SheHatzibbur Yachol Laamod Ba”), while still maintaining the guidelines against the real Issurim. In EY, the Charadim were able to make it such, due to the lack of members in the outside world (which is after all, against Charaidi Hashkafa anyway).
Telling a child that watching a TV is “poison” is counterproductive. Always tell the truth, say what the issues are (Ervah, Tznius, waste of time, etc.). You don’t want to be raising the next version of Tzaddok & Baysus.
For the OP I simply ask: Why have something in your home that will distract you from one another? At least wait until you are bored of each other! (If that CV ever happens).
Edited