Sounds like a bug. Dual monitor is explicitly supported by Lightroom (just check the webpages) so Adobe support was being lazy by claiming it worked right. Wonder if anybody else is having problems with that LR/OS combination. It works fine on my Mac but that doesn't say much about the situation on Windows.
I have used LR 5.5 on two dual-monitor computers, one Windows 7 and one Windows 8.1 and it seems ok. Are your video drivers updated, from the manufacturer’s site?
There is likely a bug, somewhere, but it may be in the video subsystem and not in LR. What is the faulting module if you see that sort of information when it crashes?
I am having a similar problem, but my workspaces swap monitors whenever I create a virtual copy. When I begin entering a keyword string, both my monitors black out a couple of times in quick succession and then come back. When I crop, the image resizes itself and the crop frame jumps around a couple of times before it settles back to the crop I had selected. A scan for 'dual monitors' on the Lightroom boards shows a number of similar reports about odd dual monitor behaviour. I am running LR 5.6 64 bit.