Your NUC is capable to work with up to four displays. So, if you have installed correctly all the Intel drivers, it should work with two displays. Be aware that the first driver to be installed should be the Intel® Chipset Device Software. Then after rebooting your NUC you may continue with the Intel Graphics Driver and all the other drivers.
If this is the case that the Chipset Device Software wasn't the first driver installed, then you are correct you should reinstall the Graphics Driver (I would say all other drivers as well), after installing the Chipset Device Software and rebooting your NUC. After rebooting your NUC, you may reboot the NUC again only once, after the last driver is installed.