This is what I'm working with. They are on the same controller, right?
https://gyazo.com/67f999d71cf5cd526500e6d9e00dfbac
See at the top where it says 'eXtensible Host Controller'? You should have multiple of those, normally. Your motherboard appears to be running a bunch of (virtual?) hubs off one USB 3.0 root, which could be causing problems (welcome to USB 3.0's notorious flakiness, and why I don't trust it, especially as a backbone). For contrast, here's a screenshot of my device manager:
Each set of ports controlled by an independent host controller, ensuring that nothing steps on each other's bandwidth.
I'd say to try putting the Scarlett and Yeti on the same host controller, and the c920s on a different one, if you only have the PCIe USB expansion card as separate.
Far as the capture card freezing the mixer goes, I really have no idea. I'd probably look at drivers first (especially if the USB expansion card is now where the cap card was before, if reshuffling happened, and you didn't un/reinstall the drivers for the cap card after moving it).
After that, I'd check into the motherboard's manual. I know there are a few out there that have 'exclusive' slot pairs; if one is populated, the other can't be used. These are pretty rare though, and more often used on the low end (stuff like ECS and similar junk) to save on traces. Which is dumb, as you can plug a 1x card into a 16x slot just fine (though I guess it makes it look like the mobo is more capable/expandable than it really is?). Doubt it's this, but worth mentioning on the off chance.