So when it tries to reach WT-RSP-D002 it fails, but if I connect to the admin$ share on the machine using the full name WT-RSP-D002.domain2.sch it works just fine.
Typically, when this occurs in a multi-domain environment it's an indication that the client system does not have DNS Search Suffix entries defined for the other domains.
The fact that it can resolve the FQDN tells us that DNS is working fine.