We had a similar issue here, while the domains were trusted etc, we had issues with deployments over on the other domain.
We built the laptops here on Domain A, so it was only applications that were specific to Domain B that need to be deployed were kept on a file server on the same domain.
The main thing is credentials are the issues.
What I have currently set up now though is on our file server (package share - we use a different location vs Lansweeper Server), we have a local user account called lsscan which has full access to that package share location and then deploy using a domain admin account used for just Lansweeper.
Since that setup we haven't really had any issues with cross domain deployments.