Hmm, I see, it’s not a real L2 bridge, it’s a hacky pretend one that relays.
I don’t have a solution for this particular situation, but I do have a suggestion on how I would do it:
Make B have its own subnet, say, 192.168.1.0/24, assuming that A is on 192.168.0.0/24. Enable DHCP and everything, it’s now it’s own full network.
Make B a client of A with a static IP, like 192.168.0.2. That makes B present on A’s network.
Add a route on A for B’s network: 192.168.1.0/24 via 192.168.0.2.
Disable NAT on B, just set A as the default route. Since A can talk to any IP on B, B doesn’t need to NAT, A can handle it for both networks.
Now, both routers should be able to exchange traffic while being responsible of their own subnet. The only thing missing would be to handle broadcasts so stuff like Bonjour/Avahi works correctly. But as a whole both layer 2 and 3 would behave a bit more cleanly with less surprises.
I think what’s going on is B sorta pretends to be A in some way to do the relaying but something is going wrong.