Connecting two routers for two separate networks on one modem

I would like to have two routers connected to one modem. The goal is to have a separate "home" network and "work" network. The reason is that we work from home and my partner has a device for work that does not play well with the current home set up running through pihole. My initial understanding was that I could just plug both routers into ports on the modem and set them up separately. The second router would live in the office away from the home router to minimize interference. When I tried it, the modem could connect and auto detect IP type on router set up, but would not populate IP and give internet. 

Modem is an Arris from Xfinity with 4 ports in the back.

Router 1 is tplink archer a7 with ddwrt.

Router 2 is tplink archer a7 with tplink firmware.

Is there a step I need to take to set up 2 networks like this? Would it help to flash ddwrt on the second router?