Allopolyploidy has played an important role in the evolution of the flowering plants. Genome mergers are often accompanied by significant and rapid alterations of genome size and structure via chromosomal rearrangements and altered dynamics of tandem and dispersed repetitive DNA families. Recent developments in sequencing technologies and bioinformatic methods allow for a comprehensive investigation of the repetitive component of plant genomes. Interpretation of evolutionary dynamics following allopolyploidization requires both the knowledge of parentage and the age of origin of an allopolyploid. Whereas parentage is typically inferred from cytogenetic and phylogenetic data, age inference is hampered by the reticulate nature of the phylogenetic relationships. Treating subgenomes of allopolyploids as if they belonged to different species (i.e., no recombination among subgenomes) and applying cross-bracing (i.e., putting a constraint on the age difference of nodes pertaining to the same event), we can infer the age of allopolyploids within the framework of the multispecies coalescent within BEAST2. Together with a comprehensive characterization of the repetitive DNA fraction using the RepeatExplorer pipeline, we apply the dating approach in a group of closely related allopolyploids and their progenitor species in the plant genus Melampodium (Asteraceae). We dated the origin of both the allotetraploid, Melampodium strigosum, and its two allohexaploid derivatives, Melampodium pringlei and Melampodium sericeum, which share both parentage and the direction of the cross, to the Pleistocene ($<$1.4 Ma). Thus, Pleistocene climatic fluctuations may have triggered formation of allopolyploids possibly in short intervals, contributing to difficulties in inferring the precise temporal order of allopolyploid species divergence of M. sericeum and M. pringlei. The relatively recent origin of the allopolyploids likely played a role in the near-absence of major changes in the repetitive fraction of the polyploids' genomes. The repetitive elements most affected by the postpolyploidization changes represented retrotransposons of the Ty1-copia lineage Maximus and, to a lesser extent, also Athila elements of Ty3-gypsy family.