multiple (required) dhcp servers causes network problems in public library

multiple (required) dhcp servers causes network problems in public library

A client of me asked me for helping with a network problem. The client in
question is a public library.
The problem: The library provide wireless internet access to the guests
via an all-in-one router provided and managed by the local telecom
provider (later refered to as internet router).
For a service they provide they need to provide internet/network
connection to an external managed accesspoint/router/all-in-one (later
refered to as service router). The service router gets it network
connection via the wan port from the internet router. This service router
also unknowingly provide DHCP services on the main network, which is in
this case a rouge DHCP.
We can't disable DHCP on both routers.
This causes that guests doesn't get internet access and the provided
service doesn't work neither.
Proposed solutions: I'm thinking about setting up a network topology where
the network is split in 2 or 3 parts with a internal router
so:
Internet router
|
\ Main network
|
\ Service network
or something like this.
I don't know how to create such topologies, are there appliances for this
or is it required to custom made this with Linux/Windows solutions?