We present detailed observations of photoionization conditions and galaxy kinematics in eleven z$=1.39-2.59$ radio-loud quasar host galaxies. Data was taken with OSIRIS integral field spectrograph (IFS) and the adaptive optics system at the W.M. Keck Observatory that targeted nebular emission lines (H$beta$,[OIII],H$alpha$,[NII]) redshifted into the near-infrared (1-2.4 micron). We detect extended ionized emission on scales ranging from 1-30 kpc photoionized by stars, shocks, and active galactic nuclei (AGN). Spatially resolved emission-line ratios indicate that our systems reside off the star formation and AGN-mixing sequence on the Baldwin, Phillips $&$ Terlevich (BPT) diagram at low redshift. The dominant cause of the difference between line ratios of low redshift galaxies and our sample is due to lower gas-phase metallicities, which are 2-5$times$ less compared to galaxies with AGN in the nearby Universe. Using gas velocity dispersion as a proxy to stellar velocity dispersion and dynamical mass measurement through inclined disk modeling we find that the quasar host galaxies are under-massive relative to their central supermassive black hole (SMBH) mass, with all systems residing off the local scaling ($M_{bullet}-sigma~$,$M_{bullet}-M_{*}~$) relationship. These quasar host galaxies require substantial growth, up to an order of magnitude in stellar mass, to grow into present-day massive elliptical galaxies. Combining these results with part I of our sample paper (Vayner et al. 2021) we find evidence for winds capable of causing feedback before the AGN host galaxies land on the local scaling relation between black hole and galaxy stellar mass, and before the enrichment of the ISM to a level observed in local galaxies with AGN.