Can the dock recognize two computers and can I switch between them? Or do I need a separate KVM switch in addition to the dock?
You want the dock to be plugged into both computers simultaneously? Not sure if that’s possible with any dock alone, but if you’re willing to unplug it from your PC to connect to her laptop then yes, any dock should work.
I would add that a lot of the cheaper docks may give you problems with one thing or another- one of your monitors might not work (even if the dock has two ports), the power may not pass through at the right rate for the laptop, etc. It may be worth spending money on a good one.
Fwiw, I have
this one at work and it’s excellent. That specific model might not work for your desktop as it’s only USB-C, but Dell may have others that could work for you. Note that they have different options that look the same but lack one or two ports. For example, the one above doesn’t have an audio port- they charge extra for that.