gt 720m is a fermi device:
[url]https://www.notebookcheck.net/NVIDIA-GeForce-GT-720M.90247.0.html[/url]
That device is no longer supported by recent drivers or recent CUDA toolkits. (on any operating system)
Installing a newer driver will result in error 43 on the Fermi device. (there would be an error on any OS)
Installing an old-enough driver that understands the Fermi device may not understand the newer Pascal device (1050ti), in which case the Pascal device would show an error 43. (there would be an error on any OS)
You cannot have 2 NVIDIA GPU drivers loaded and active at the same time, in any operating system.
If this were my system and I were desperate for this to work, I would search for a new-enough driver that recognized the 1050ti, but not so new that Fermi support had been dropped. The most recent drivers in the R384 or possibly R390 driver branch might fit that description. You would have to do some searching and testing. You would basically need to search for such a driver (R384 or R390, no later) that was published by NVIDIA after the 1050ti was released to the market.
However such drivers will not support the latest CUDA toolkits (e.g. 10.x)
And I’m not guaranteeing success, just outlining what I would try. A better option of course is to ditch that GT720m and get a newer base system, for the most flexibility and latest support.
And windows update does not know how to negotiate this minefield, and if you allow it to be active it may disrupt your best efforts. And yes, when backtracking drivers it is usually best to perform a full uninstall or clean sweep with a utility like ddu.
I suppose another option might be to just install a new driver, let it work when the egpu is plugged in, and when not, acknowledge that the GT720m is in an error state and use the igpu instead. There might even be a setting in your system BIOS to disable the dgpu.