Dual monitoring with a TV, weird issues

[Xeogred]

I use a splitter and it fixed all those issues mentioned above.
https://www.monoprice.com/product?p_id=8204.
Works great.
Mine isn't a smart tv, but having a regular LCD and a big screen plasma into 2 different hdmi ports on my computer was causing all kinds of headaches just like OP. As long as the computer thinks I only have one display, all is fixed.

That seems kind of funky, so instead of having the computer HDMI go directly to the TV, I should put it in my splitter? I have one for all my consoles. It's been nice to have them separated since the computer HDMI out source is always "on" to switch to. I guess I'll give it a shot, but that might give me issues when I boot up consoles. I can switch the sources on my splitter but it does get kind of finicky about it.

[Anapan]

It is not a switch, it is a splitter - it sends the same picture from one source to two screens.
I think as far as my computer is concerned, my big screen is always on and plugged in to it, as the sound of USB being unplugged only happens when the splitter gets unplugged.
I use that same splitter for all my consoles except for the PS3 which doesn't play well with most of my equipment. I have a switch earlier in the video chain as well.