I don't think there are any political overtones in the NM verse. I remember that there was a version sung to children and I think these two verses are from that one, but I don't remember any of the song.
In New Mexico, pinto usually means 'spotted,' but painted is OK too.

Two stars in their eyes is, I think, correct. The line in Spanish might have been incorrectly rendered by Loomis. On the other hand, New Mexico has some peculiar idioms surviving from Spain of 400 years ago.