Gateway. Does the system properly know how to get outside of its subnet.
Gobo
Check your route table and arp cache (for gw). Are you using dhcp?
At first I was going to say there is ATI. Then I realized I hadn't heard about ATI in a while and looked up what happened to it. Then I realized... I'm old.
For some reason the SMB2 theme song is stuck in my head all the time. Something about the jazziness of it.
Your current default gateway for your existing 192 network needs to have a route to your 10 network. Otherwise none of your devices in the 192 network know where to go to access the 10 network.
If it is caching you can always set a ttl to a lower value like 5 seconds. And systems should be clearing the dns cache on a new ifup.
Set up an internal dns server that will resolve your specific host name to an internal ip and forward everything else.
If you just want a specific site, you can use bind and response policy zones. The advantage of this is that you can now configure your dns server to take advantage of block lists on the internet and block malware/ads/tracking domains.
Setup nginx as a v6 to v4 reverse proxy. Or the inverse if you have a public v4 in a vpc to use as a dmz.
/usr/lib or /usr/lib64 or /lib (some distros) or /lib64
Some things (like hosts file) are in /etc. /etc mostly contains configs.
It's github. Submit a PR
Then I'd say get a pcap from the pfsense interface and see what's going on. Is the systems Mac still in the fw arp table? . If you think it's a system fw problem, try disabling the local fw and see if things work