I have heard from one of the gedoilim (I think it was R’ Matisyahu shlita), that the shabbos table requires preparation. The same way a teacher prepares lessons, and a maggid shiur/lecturer (lehavdil) wouldnt stand before his audience without preparing precisely what he will say, so too every table leader of a shabbos meal MUST prepare divrei torah, a story or two etc to keep everyone interested. This keeps the family at the table and prevents the lashon hara seeping in.
Also, the shabbos meal is not a time for interogating the kids with questions on the parsha. That can be done any other time on shabbos. The meal should be a relaxed and pleasant enviroment, where adult and children alike are happy to partake.
Perhaps with these ideas the kids wont be tempted to curl up on the couch with a book out of boredom. And if a kid does fancy 20 minutes reading, what can happen? Is it the end of the world?
Take a chill pill, relax and be happy your kid comes to the shabbos table in the first place. There are those who unfortunately cry every shabbos at the absence of their kids because they are “elsewhere”.