It is common in songs, and it is not specific to children’s songs.
In the first case, the pitch of the lyric line is probably something like:
> (G) (G) (G) (G) (G) (F#) (G) (E) (F#) (D)
but if you try to sing this as it is, there is a problem: gemination is not a sound but just a pause, and you cannot sing it with any pitch. Therefore, the vowel preceding the gemination is prolonged to fill the first part of the mora which should filled by the gemination:
> (G) (G) (G) (G) (G) (F#) (G) (E) (F#) (D)
I did not check the other two videos, but I guess that they arose for the same reason.