Get a list of all DCs and use that in a ForEach-Object loop. Use the Get-ADComputer cmdlet to look for the computer name in the filter and add the "-Server" parameter using the name of the DC in the iteration of the loop.
But this isn't going to help you troubleshoot trusts, or replication. There are GUI and command line tools for that. Here's one of each:
get-use-active-directory-replication-status-tool
repadmin-how-to-check-active-directory-replication
If you want to use PowerShell, there are ways to do that, too: 326364