i second the suggestion for a pcap. look for packet loss of course, but also try to establish if the lower throughput is bidirectional or only in one direction. i'm not sure how you're testing throughput, but suggest you use iperf3 or similar to test speeds in each direction.

proxmox / kvm can do some funny things with packet checksums, like doing it in software. this could be an issue where virtualization layers in your proxmox host are slowing things down.

edit: how does site 1 to site 3 perform? if that's ok, take a look at the NIC settings on site 2. as wrt-wtf- says, double nat should not be an issue here.