BatchPatch works fine in a cross-domain cross-forest config. We use it like that all the time. The error you are receiving is not a BatchPatch error per se. It’s from Windows (being passed through by BatchPatch). It could be something with your domain controller config or DNS or SPNs or forest trust relationship etc. It has nothing to do with BatchPatch. I would suggest you review the various suggestions/fixes/resolutions described by people in forums on the web:
https://www.google.com/search?ei=mLOGW8OID6bZ5gLHx4XYBg&q=the+security+database+on+the+server+does+not+have+a+computer+account+for+this+workstation+trust+relationship