DHCP over two routers

[Bad boy Warrior]

Not sure what options i have here

I have Router 1 and Router 2 - Router 1 is the main router which is used to allow users to connect to the internet via wireless but is linked to router 2 via a cable. Router 2 is disconnected from the internet as its used as a slave router.

Before, router 1 was introduced router 2 was the main access between clients, server and the default gateway for internet access, but no DHCP was used.

Since we now have two routers is it possible for me to configure DHCP on the server (and disable it on router 2) so all IPs are distributed from the server and of course setting the default gateway to router 1 from the server? Also would this cause any issues for any "outsiders" to connect their laptop (which is not part of the domain) and pick up an IP from router 1?

Thanks

[Tripredacus]

It may be simpler to replace Router 2 with a managed switch. A standard switch will give you less options but will be cheaper.