What you define as light gaming? Is something that will run without a gpu?
Could go with a couple of approaches - dedicated thin clients can be found on e-bay for not too many dollars. They usually come with RDP clients which will allow you to connect to the VMs via remote desktop (but will need them to be running Windows Pro or higher or a Linux distro with XRDP installed).
Option b) is a roll your own option. Again you could use the thin clients (just might be a bit of extra work) or get a mini pc (say Dell USFF) with an i3 or i5. You won't need that much oomp at the thin client end. Could even do with a Rasberry Pi or other SBC but might not be any cost savings on the hardware and you're working cross platform.
Not sure if your kids are the dual monitor stage but if so, a thin client or USFF PC will allow you to connect multiple monitors. Mileage may vary on SBCs.
The idea is to use iPXE/PXE for remote booting the thin clients. That gives you a build/update once deploy many approach.
There's ltsp (ltsp.org) which I use. You build up a system with the apps you want (in my case the Proxmox VDI client, Remmina for RDP, Parsec & Moonlight for accelerated graphics support for when I play games, NoMachine, AnyDesk and Firefox) though you probably don't need all those. To keep the size down build from basic Linux distro (Ubuntu Server, Debian net install) and use a lightweight desktop manage (XFCE is ideal). Build it, boot and off you go.
Or you easily build one with Alpine Linux (apalard.net has tutorial - it's geared at the Proxmox VDI client but the general approach would work in your case).
Only problem with Alpine is you pretty much have to install again to update everything. LTSP, update the Linux distroy, rebuild the ltsp image and reboot (so 2/3 commands).
If unRAID used KVM (which i think it does) you can use Spice/Virtviewer for remote access. One advantage with Spice is the ability to pass through USB devices which you don't get with RDP.
Reason I asked about the gaming is you'll then need to dive in to GPU pass through and use of Parsec or Moonlight to take advantage of it.