In your case, the connector is being invoked via the gateway (IDP URL is the FQDN).. the URL in the browser has not changed (it has remained the FQDN, right?). So, the cert on the connector doesn't matter.
Ignoring the "Failed to initialize Java keystore handling." error you saw on the connector, is there any functionality problem you are seeing?
Is the browser prompting you to accept a cert? Is the login successful?