One Slate, one Brume, even one cable and one port on each device if you use VLANs!
(And possible to do with a single cable without VLANs as well)

Hotel Wireless
       |
Slate STA interface <--- VLAN mmm ---> Brume "VPN out" interface
Slate AP interface  <--- VLAN nnn ---> Brume "VPN in" interface
       |
Your clients