I have followed all the steps found at the link below to try and set up a multi-Net setup exactly as described, except there is no static link between the the entities in the router (I want them kept separate):

https://www.tp-link.com/us/support/faq/887/

The router is a TL-R600VPN and the switch is a T1600G-52PS firmware (4.0.3 Build 20190516 Rel.38446(s))

I have the vlans labelled as 10 and 20 instead of 1 and 2. I have vLan 10 set up on port 17 and the PC attached to it gets the right IP address for the vlan. However, the PC cannot get to any IP address outside of its subnet range. The routing seems to be broken in the switch for that setup. I can ping from the switch to 192.168.0.1 (router as gateway) and to the PC on its given address. The PC can ping the switch on the DHCP interface address, but the pc cannot get DNS information nor can it ping 192.168.0.1 or something on the wider web like 8.8.8.8. What step am I missing?

As an FYI, I can attach the PC to another port on the switch and it will get an IP address from the router (192.168.0.100) and have internet access just fine. 

Thanks,

B