Expansions of CAG/CTG trinucleotide repeats in DNA are the cause of at least 17 degenerative human disorders, including Huntington's Disease. Repeat instability is thought to occur via the formation of intrastrand hairpins during replication, repair, recombination, and transcription though relatively little is known about their structure and dynamics. We use single-molecule Förster resonance energy transfer to study DNA three-way junctions (3WJs) containing slip-outs composed of CAG or CTG repeats. 3WJs that only have repeats in the slip-out show two-state behavior, which we attribute to conformational flexibility at the 3WJ branchpoint. When the triplet repeats extend into the adjacent duplex, additional dynamics are observed, which we assign to interconversion of positional isomers. We propose a branchpoint migration model that involves conformational rearrangement, strand exchange, and bulge-loop movement. This migration has implications for how repeat slip-outs are processed by the cellular machinery, disease progression, and their development as drug targets.