Aries — “Who know one?” is a lot of of fun to sing, as are all the rest of the Uncle Moishy songs, especially the earlier ones.
PBA — I better understand your comment now that I see how you understood the word “entertain.” I did not get the impression that “entertain” meant “get them to stop screaming”. I understood the question as to how to involve and excite your kids during the meal. I personally think this is a great question that more parents should be asking. It bothers me when the bulk of a Shabbos meal is geared only to adults, so that the kids can only last a few minutes. I firmly believe that a Shabbos meal can be structured in a way that even young kids can participate for more than a few minutes (although I agree that 20 minutes for a preschooler is probably the max, not counting eating time.) Why is your approach to “forget entertainment”? What is wrong with coming up with entertaining and meaningful activities such as stories and songs as described by the OP?
I remember a young family I used to eat meals by when I was in seminary who had a ton of guests, and their policy was they only had guests one meal each Shabbos (barring emergencies), and the other meal they kept family only so they could gear the meal towards their young kids. Personally I think that is a beautiful concept.