Navigating a complex x11 setup?

I have a laptop that is perfectly serviceable.  It has Intel Integrated
graphics _and_ nVidia Quadro graphics.  The idea being that only
applications that need the Quadro use it.

The Intel is: "4the Gen Core Processor Integrated Graphics Controller"
cpu: i7-4800MQ
The nVidia is: GK106GLM (Quadro K2100M)

 For some time, I've used the Intel driver and the nVidia secondary
driver.  This has worked well and still appears to work... but not
entirely.  Sometimes moving things about the screen leaves artifacts ...
other times, it's  a mess.  A full refresh fixes it, mostly.

With another machine, I was told to use the modesetting driver --- but this
fails to find a /dev/dri entry.

Help?