I resolved the problem.

I'm an idiot. Well, not really, but that's how I feel now.

My new laptop has two USB ports, one on each side. I thought they were both USB 3. Actually one of them is USB 3 and one is USB 2. I had the dock plugged into the USB 2 port. When I realized this after looking in the manual for something else, I shut down the laptop, moved the dock to the USB 3 port and rebooted with the monitor plugged into the docks HDMI port. It took a few seconds for everything to setup but Win 10 detected the second monitor and duplicated the image to it.

I think this will probably resolve my issue with the Ethernet drops, but that will take some more testing to determine for sure.

One reason I didn't check this initially was because I was getting 60 mbps over the hardwired network connection, which is where my cable modem makes out. Latency does seem a lot less now that I have the dock correctly connected.

So thanks for your help. I figured that the least I could do is comeback and share the resolution in case you see the problem again, embarrassing as the mistake was.

Thank you for taking the time to post the answer Richard.
This could (and probably will) happen to anyone!