\begin{document}$ D_s^+\to \eta \omega\pi^+ $\end{document}, \begin{document}$ D^+\to K^0_S\pi^+\omega $\end{document} and \begin{document}$ D^0\to K^-\pi^+\omega $\end{document}. In this work, we investigate the contributions of the subprocesses \begin{document}$ \rho^+\to \omega\pi^+ $\end{document} in these Cabibbo-favored decays \begin{document}$ D \to h\omega\pi $\end{document}, with \begin{document}$ \rho^+= \{\rho(770)^+, \rho(1450)^+, \rho(770)^+\&\rho(1450)^+\} $\end{document} and \begin{document}$ h=\{ \eta, K^0_S, K^-\} $\end{document}, by introducing these subprocesses into the decay amplitudes of relevant decay processes via the vector form factor \begin{document}$ F_{\omega\pi} $\end{document} which has measured in the related τ and \begin{document}$ e^+e^- $\end{document} processes; we provide the first theoretical predictions for the branching fractions of the quasi-two-body decays \begin{document}$ D_s^+\to\eta[\rho^+\to]\omega\pi^+ $\end{document}, \begin{document}$ D^+\to K^0_S[\rho^+\to]\omega\pi^+ $\end{document} and \begin{document}$ D^0\to K^-[\rho^+\to]\omega\pi^+ $\end{document}. Our findings reveal that the contributions from the subprocess \begin{document}$ \rho(770)^+\to\omega\pi^+ $\end{document} are significant in these observed three-body decays \begin{document}$ D_s^+\to\eta \omega\pi^+ $\end{document}, \begin{document}$ D^+\to K^0_S \omega\pi^+ $\end{document} and \begin{document}$ D^0\to K^- \omega\pi^+ $\end{document}, notwithstanding the contributions originating from the Breit-Wigner tail effect of \begin{document}$ \rho(770)^+ $\end{document}. The numerical results of this study suggest that the dominant resonance contributions for the three-body decays \begin{document}$ D_s^+\to\eta \omega\pi^+ $\end{document} and \begin{document}$ D^+\to K^0_S \omega\pi^+ $\end{document} are originated from the P-wave intermediate states \begin{document}$ \rho(770)^+ $\end{document}, \begin{document}$ \rho(1450)^+ $\end{document} and their interference effects."> Contributions of <i>ρ</i>(770,1450)→<i>ωπ</i> for the Cabibbo-favored <i>D</i>→<i>hωπ</i> decays -
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