The requirements to use DameWare in a cross-domain environment are functionally no different than it is to use any other application or service in a cross-domain environment.
If you can map a drive to a resource in Domain2 using your Domain1 password, everything else should work exactly the same.
If you cannot map a drive to a resource in Domain2 using your Domain1 password, the problem is not with DameWare. :-)
These are standard Microsoft Windows cross-domain authentication policies that apply here. Pretty much anything anybody has written about cross-domain access in the past 10 years would be applicable. Based on everything I've read here, I'd go back and explicitly verify that there is a valid parent-child trust in place. Sometimes I've seen people create subdomains, in name, but not actually create them as a child of the parent domain. It looks like a parent-child relationship because of the naming, but internally in Active Directory it's not.