networking - Public wireless access point on a private network

hopefully someone has an idea on this.

I have a business with a private wired network, but want to provide a public wireless access point for the internet. Users on this AP should not be allowed to see anything on the private network.

I have tested this using 2 routers I have in my house, managed to get 2 networks up like so

Modem -> Router 1 -> Private Computers

            ^-> Router 2 -> Public computers

However, router 2 should be acting as the public AP, but anything on it can still ping anything connected to the 1st router.

I don't have the ability to change the Modem to the public side, so the solution needs to just be able to plug into the private network and just provide a public LAN that is separated from the main (private) LAN.

Basically just looking for a product/router that will allow this. I have my eye on a Netgear fvs318 which I think will do the trick, but I'm unsure, so some advice/help/recommendations would be great.

Thanks!