

I’ve also looked at an idea liked this, what stopped me was anti-cheat engines. They will usually block playing in a VM and there is no real way to trick them into thinking you’re not in a VM.
If that’s what works best for you, I don’t agree that having multiple boxes for different purposes linked by network is ugly. This is often what you see in enterprise and should bye plenty fast for your needs.
An full computer is also not a bad idea, if you want a gpu for transcoding it could be good. Honestly I found in most cases CPU transcoding with modern CPUs was quite good. If you go the GPU route, I would simply look for a used, cheap GPU it should do the trick!
Opinion from someone with divorced parents: it’s fine. The “stability thing” isn’t that important, what is is a healthy relationship between the 2 parents, which you seem to have. My parents kept a good relationship and are still friends to this day, and that really helped, more than if they stayed in the same house or if didn’t let their new partners move in.
Having both your ex-wife and new partner in the same house could cause issues, but not because of the stability, because of conflicts it could bring. This is what is difficult for kids, having to deal with parents in conflict. If you believe you can make this work, that they’re both grown up enough to live together and that the roles vis-a-vis the kids are clear I would say go ahead, when I was a kid I was happy to see my parents getting new partners and becoming happier!