Expanding symmetric functions in the basis of Schur functions is an important, if difficult, problem with applications to representation theory and geometry. In particular, we will be concerned with expanding functions related to the modified Hall-Littlewood polynomials, a remarkably useful basis for the symmetric functions adjoined by the variable t. While Lascoux and Sch\"{u}tzenberger gave a description of their Schur expansion using the charge statistic in 1978, we will give a new expansion as a sum over a subset of the Yamanouchi words. We will also give related results for several other families of polynomials. The source of these results is the theory of dual equivalence graphs, as first introduced by Assaf in 2007. By associating a function to a graph and each component of said graph to a Schur function, dual equivalence graphs have become an intriguing new tool for answering questions about Schur positivity. Along the way, we will pose several open problems and conjectures, as well as presenting some pretty pictures.