So in love

The whole song is in the play, in the dressing room scene. Where Kathryn Grayson just reprises it in the movie, the play shows a split set of both Fred's and Lili's dressing rooms after Lili has received the flowers (meant for Lois) and Fred is eyeing the champagne cork (an old keepsake) which was part of an earlier verbal exchange between them. When the song ends, they are both singing it in a counter-point arrangement, but of course, not in the same room to know they are both remembering the same thing- though they are back-to-back up against the walls. (If you can find it, check out the television broadcast of the London production with Brent Barrett and Rachel York, which was taped in 2003, I believe, for PBS' Great Performances.)

I may be wrong, but I think the OP was asking where "So In Love" was supposed to have fit into their "Taming of the Shrew" musical. At the beginning of the movie in Fred's apartment, Cole Porter gave the song to Lilli to sing with Fred, saying it was the love song from his new musical. I'm guessing we're supposed to understand that it's a love song between Kate and Petruccio, presumably after he "tames" her, but I think the only other time we actually hear it is when Lilli sings a short reprise in her dressing room. What a gorgeous song.

In the original Broadway production, the song is not in "the show", nor is it ever stated that it is a number from "the show". That whole scene in Fred's apartment was comtrived for the 1953 film version. The number is first sung by Lilli in her dressing room (which ends up being a reprise in the film), then it is later reprised in the second act by Fred after Lilli leaves. As far as the film goes, I don't think we're supposed to worry too much about where the song would have fit into "the show". We're just supposed to take their word for it that it does.