Whether or not it's part of a larger script, you didn't answer the questions. So, let's assume that you have NOT tried using the -Server parameter and a specific DC in the "other" domain. Neither have you said whether you can get the computer object by using Get-ADComputer without using the -Server parameter and the name of a DC in the "other" domain.
So, let me suggest something (assuming that all your domains are in the same AD forest): try "Get-ADComputer <name> -Server <GlobalCatalogServer>:3268 (you can use Get-AdDomainController to find one rather than hard-code it; use the parameters "-Discover -Service GlobalCatalog")
If that finds the computer, get the distinguishedName value and extract the domain name from that and find a DC using "Get-AdDomainController -Discover <domain-name". Then use the (or one of) the DC name/s in the Remove-ADComputer cmdlet.