So your issue is LAN ip address assignment for the esp and the rpi behind your "travel router" (whatever that means)?
Should be an easy issue to solve if both esp and rpi support fixed ip address assignment: just assign them to addresses within the scope of your travel router's lan side.
eg: if the router's lan address (aka gateway address) is 192.168.1.1, assign fixed ip addresses to the esp and rpi like 192.168.1.100 and 192.168.1.101.
The rpi for sure supports fixed address assignment, but if your esp code does not, dig into your "travel router" guide and see if you can have it associate an ip address with a mac address and always assign the same ip address to the esp.
Once you get that far, configure your agent web pages to look for each other at the appropriate addresses...
Cheers!