Is Edge officially supported? I know when I have issues with Chrome there is usually a Chrome update that needs applied, maybe it's the same with FF?
I don't know what "claimed secure browser" is but is it something you can temporary disable and test again?
The router on the other vlan that is forwarding the DHCP request automatically adds the needed info to tell the DHCP server what scope the request is coming from.
What router are you using? For Cisco you need a helper-address pointing to your DHCP server.