correct syntax for putting a powershell script into a variable with double quotes

Invoke-VMScript -ScriptText accepts only a string containing PowerShell code, and has no support for separately passing arguments to that code.

The implications are:

• In order to include variable values from the caller's scope you indeed need to use string interpolation (via an expandable string, "..."), as you have attempted.

  • Note that this situationally requires embedded quoting around reference to caller variables whose values may contain spaces or other special characters; e.g.
    "... -Foo '$foo' ...")

• As Mathias R. Jessen points out, variable references you want to be evaluated on the target machine must have their $ sigil escaped as `$ so as to prevent premature interpolation on the caller's side; e.g. `$Using:sqluser

There's a catch, however:

• Use of string interpolation imposes limits on what data types may be embedded in the string, as not all data types have string-literal representations that are recognized as the original type.

  • In your case, the caller-side $cred variable contains a [PSCredential] instance, which does not stringify meaningfully (and cannot, for security reasons): it meaninglessly expands to a verbatim string value of System.Management.Automation.PSCredential, i.e. the instance's type name.
    In other words: you cannot pass credentials this way.

  • A potential workaround requires up-front work on the target machine: You can try to save the credentials in encrypted form to a file and then deserialize that file at invocation time via Import-Clixml.

    • See this answer for a demonstration, and this answer for the security implications of this approach.