In many kindergartens and preschools, both boys and girls sing at the end of davening, "We want Moshiach, we want Moshiach now..."
Was this instituted by the Lubavitcher Rebbe?
As far as I know about the song, "we want moshiach now" it was first sung in 1980 by a group of campers. The Rebbe began clapping along as approval and afterwards encouraged singing it. The song itself was written by campers and then received the Rebbe's approval after it was first sung in front of him.
As to why this kindergarten does this after davening... This is not part of the nusach and is something this kindergarten decided to include. Perhaps others do the same perhaps they have other songs they chose to use. It should not be surprising that a kindergarten has singing making davening more geared to small children who might otherwise have difficulty focusing for a long time during shachris.