I understand you are having problems to connect your computer to a monitor using Thunderbolt port.
Based on your description, it seems that your computer has switchable graphics. This means that your system have the Intel® HD graphics controller and a dedicated video card, in your case the Nvidia Chip and the computer may select what Graphics card wants to use or you also have the possibility to select what Graphics controller you want to use.
Since your computer has this special configuration, it requires special drivers. We as Intel® provide the hardware to the system manufacturers like Dell, HP, Toshiba, Acer, etc… and they will design and create custom drivers specifically for their systems. Due to this, it is necessary to get the drivers directly from the system manufacturer.