What kind of conflicts would rise if you had your network come into a firewall/router and split to 2 systems and another firewall/router that split to an additional systems?

Why?

1.) Because I need another router for this section of the house.
2.) Because if the secondary network would be more secure, it would work out as a plus since the second router would be installed inside my office.
3.) If there would be issues, then I would go with a basic switch.