Resonant structures in the dipion mass spectrum from ${\chi }_{c1}\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi$ decays, produced via $B^{+}\to K^{+}{\chi }_{c1}\left(3872\right)$ decays, are analyzed using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. A sizeable contribution from the isospin conserving ${\chi }_{c1}\left(3872\right)\to \omega J/\psi$ decay is established for the first time, $(21.4\pm 2.3\pm 2.0)\%$, with a significance of more than $7.1\sigma$. The amplitude of isospin violating decay, ${\chi }_{c1}\left(3872\right)\to {\rho }^{0}J/\psi$, relative to isospin conserving decay, ${\chi }_{c1}\left(3872\right)\to \omega J/\psi$, is properly determined, and it is a factor of 6 larger than expected for a pure charmonium state.