How can I run a remote EXE with a variable path and arguments?

A single string such as 'Path.exe /switch1 /switch2' mixes the path and arguments together. For a native command, store them separately. Each argument can be its own array element, then splat the array:

$path = 'C:ToolsSetup.exe'
$args = @('/quiet','/key:12345')

Invoke-Command -ComputerName $computerName -ScriptBlock {
& $using:path @using:args
}

If the installer launches child processes, make sure the process you wait for actually represents the complete installation. Start-Process -Wait waits for the launched process and its children, while waiting on the process separately may only wait for the immediate executable.

Use parameters in the remote script block to receive the values passed through -ArgumentList. Keep the executable path separate from its arguments, and invoke the executable with the call operator:

$exePath = 'C:InstallersPath.exe'
$exeArgs = @('/switch1','/switch2')

Invoke-Command -ComputerName $computerName -ArgumentList $exePath,$exeArgs -ScriptBlock {
param($ExePath,$ExeArgs)
& $ExePath @ExeArgs
}

You can also use Start-Process when appropriate:

Invoke-Command -ComputerName $computerName -ArgumentList $exePath,$exeArgs -ScriptBlock {
param($ExePath,$ExeArgs)
Start-Process -FilePath $ExePath -ArgumentList $ExeArgs -Wait
}

The -Wait is important for installers because otherwise the remote command may finish while the installer is still running, and the process can be terminated when the remoting session closes. With -ArgumentList, the script block must define parameters with param(); the original local variable names are not automatically available remotely. $using:exePath and $using:exeArgs are another option, but explicitly passing parameters is usually clearer.

Invoke-Command runs the script block in a separate scope, so local variables need to be passed in or referenced with $using:. A parameter object is useful when there are several related values:

$install = [pscustomobject]@{
Path = 'C:ToolsSetup.exe'
Arguments = @('/quiet','/key:12345')
}

Invoke-Command -ComputerName $computerName -ArgumentList $install -ScriptBlock {
param($Install)
Start-Process -FilePath $Install.Path -ArgumentList $Install.Arguments -Wait -PassThru
}

The key points are defining param() in the script block, separating the file path from its arguments, and waiting for the installer when the remote session must remain active until installation completes.