The decays $B+\to J/\psi \pi +\pi -K+$ are studied using a data set corresponding to an integrated luminosity of 9fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ collected with the LHCb detector in proton-proton collisions between 2011 and 2018. Precise measurements of the ratios of branching fractions with the intermediate $\psi 2(3823)$, $\chi c1(3872)$ and $\psi (2S)$ states are reported. The decay of $B+\to \psi 2(3823)K+$ with $\psi 2(3823)\to J\psi \pi +\pi -$ is observed for the first time with a significance of 5.1 standard deviations. The mass differences between the $\psi 2(3823)$, $\chi c1(3872)$ and $\psi (2S)$ states are measured to be $$ \begin{array}{rcl} m_{\chi_{c1(3872)}} - m_{\psi_2(3823)} &= & 47.50 \pm 0.53 \pm 0.13,\mathrm{MeV/}c^2,, \ m_{\psi_2(3823)} - m_{\psi(2S)} &= & 137.98 \pm 0.53 \pm 0.14,\mathrm{MeV/}c^2,, \ m_{\chi_{c1}(3872)} - m_{\psi(2S)} &= & 185.49 \pm 0.06 \pm 0.03,\mathrm{MeV/}c^2,, \end{array} $$ resulting in the most precise determination of the $\chi c1(3782)$ mass. The width of the $\psi 2(3823)$ state is found to be below 5.2MeV at 90% confidence level. The Breit-Wigner width of the $\chi c1(3872)$ state is measured to be $$ \Gamma^{\mathrm{BW}}{\chi{c1}(3872)} = 0.96^{+0.19}_{-0.18}\pm0.21 \mathrm{MeV},$$ which is inconsistent with zero by 5.5 standard deviations.