Using a similar framework to \([7]\), we construct a family of relative difference sets in \(P \times ({Z}_{p^2r}^2t)\), where \(P\) is the forbidden subgroup. We only require that \(P\) be an abelian group of order \(p^t\). The construction makes use of character theory and the structure of the Galois ring \(GR(p^{2r}, t)\), and in particular the Teichmüller set for the Galois ring.