Stephen, I believe if your code attempts to connect to both (or multiple) domains with multiple Connection Strings it would be possible, or if one of your Domain Controllers has been joined to the other Domain (or vice versa) you might be able to get away with only asking one for the authentication and it would check both (not 100% on this to be honest, it's been awhile...).
The error you have stated makes me think the code is having issues connecting to the LDAP endpoint (domain controller). Have you specified the fully qualified domain in the LDAP connection string? As in typcially you would see
LDAP://Domain/DC=Domain but sometimes you need the whole thing
If you use ADExplorer on your windows server that is hosting the IIS Site (assuming you are on premise) can you view both domains from that tool on that server ?