Looking for guidance on a design with one subnet and multiple VLANs

Hi everyone,

I'm the system admin. at my company that is responsible for swapping Internet providers. We got ourselves a LAN 2 extension to connect our two facilities to our HQ. I'm struggling to come up with an elegant design that maximizes utilization of switches and minimizing changes to the network. My knowledge in networking is not strong (crashing through the Cisco CCNA ICND1 book to get up to speed) so I was hoping to ask for advice from this subreddit.

I've created a network diagram for reference that can be found here.

Some points:

• Our ISP provides traffic coming from site #2 with VLAN 100 and traffic from site #3 with VLAN 200.
• Switch SW-1 has one access port for VLAN 100 and one access port for VLAN 200. One port is trunked that goes to the ISP.
• I'd like to maintain subnet 192.168.20.0/24 across all 3 facilities.
• Presently we have majority of hosts connected to SW-Access. No VLAN tagging performed on this switch.

The problem I’m struggling is if frames coming from Site #2 destined to Site #3, it needs to be routed from VLAN 100 to VLAN 200. First thought that comes to mind is to use IP routing. However, if all 3 sites want to use the same subnet address, then in theory, this isn't possible.

The other option I thought was to create a physical link between the access ports on SW-1 to SW-Access. In theory, with ARP and layer 2 routing, this should work. The problem now is SW-1 is a 48-port switch. I'd like to connect more hosts (maximize utilization of switch) that are part of the same subnet. How could those hosts connected to SW-1 on VLAN 1 (native) ports communicate to the access VLAN ports (on the same switch)? In theory, I could create a physical link from SW-1 to SW-Access on VLAN 1 (native). But that seems inefficient to introduce one hop.

Any suggestions or advice is welcomed. Thanks everyone.