No, you can’t run both of the add-ons at the same time. You should remove the core add-on and integration and make sure you re-install the integration according to the ZUI add-on documentation. https://github.com/hassio-addons/addon-zwave-js-ui/blob/669fe696d1d421a04161180fdfbb7c83634eaa9e/zwave-js-ui/DOCS.md#setting-up-the-home-assistant-z-wave-js-integration