I've been having the exact same issues.
I never had much issues getting OpenVPN to work with a passphrase configuration in the past, but as soon as I moved to a certificate-based tunnel I've been having the issues you've described, despite apparently having the correct firewall rules and routes configured. Traffic only flows properly one way.
On the reverse direction, Site B seems to be unable to exit the tunnel back to the LAN.
Have you ever figured out what was wrong in your case? Perhaps that would help me...
I never had much issues getting OpenVPN to work with a passphrase configuration in the past, but as soon as I moved to a certificate-based tunnel I've been having the issues you've described, despite apparently having the correct firewall rules and routes configured. Traffic only flows properly one way.
On the reverse direction, Site B seems to be unable to exit the tunnel back to the LAN.
Have you ever figured out what was wrong in your case? Perhaps that would help me...