Not a broadway show, but in Disney's "Home on the Range" (scored by Alan Menken) there is a cute infectious song all ABOUT and WITH LOTS of yodels. it's called something like "Yodel-idle-eedle-idleooo"
"As for Kristin yodeling on the word popular, I just like yodels, and Kristin is from Oklahoma. So maybe I was thinking unconsciously of country-western music, and I knew she could do it"- Stephen Schwartz (Wicked: The Grimmerie, Popular p78-79)
HI HELLO I'VE READ THROUGH THIS ENTIRE MESSAGE BOARD HOW HAS NO ONE MENTIONED "ROLL IN THE HAY" FROM YOUNG FRANKENSTEIN???? OUR VERY OWN SUTTON FOSTER YODELED THROUGH THE ENTIRE SONG ON BROADWAY. if you want a broadway song with yodeling, go check that one out. you will not be disappointed.