This Could Be The Night, 1957, directed by Robert Wise. Paul Douglas plays the nightclub owner, Jean Simmons the school teacher/secretary and Tony Franciosa as the love interest. The teacher does not fall in love with the owner, who ends up feeling quite protective of the teacher, but with one of his associates.
I believe the hymn the boys sang was O Sing Unto God. The arrangement is probably not commercially available and I don't think there is a soundtrack available.
I've heard various reasons given for this "jump cut". Ranging from the master had deteriorated and a few frames were missing by the time home video technology came to be; to censorship a la The Pirate; to Kelly liking the performances of parts of two different takes, requiring that they be edited together at the least intrusive moment.
It's hard to believe that Kelly would let this go intentionally -- it is so noticeable. And he spoke about the studio removing a dance sequence from The Pirate because it was thought to be too risque. If it had been about censorship he would have most likely spoken about it. It seems logical to me that with the stature of SITR if there were a real "story" behind this, it would be well known by now. My vote is that the master had fallen into disrepair like so many films and a few frames were lost.
I disagree that it would have anything to do with contradicting the romance between Don and Kathy. If that were the case, the whole Broadway Ballet would be a contradiction. A kiss would hardly make this sequence more senuous or suggestive than it already is. Unlike the ballet section in On The Town, the Broadway Ballet is not a recap of the story or of the characters. It has nothing to tell us about Don and Kathy.
A Star is Born, The Harvey Girls, Til The Clouds Roll By and, of course, The Wizard of Oz are all available on DVD. Also, most, if not all, of The Judy Garland Show is available in both episodes and collections.
It was Lisa Kirk, not Phyllis Kirk, who did most of the singing for Rose. Lisa also was the original Bianca in the stage version of Kiss Me, Kate in 1948
There is an online petition "urging" this very bad idea not to come to fruition. Not that it will actually stop anyone from doing anything, but it does feel good.
http://www.petitiononline.com/no2jlo