As noted in previous responses, using "$MyInvocation" is subject to scoping issues and doesn't necessarily provide consistent data (return value vs. direct access value). I've found that the "cleanest" (most consistent) method for getting script info like script path, name, parms, command line, etc. regardless of scope (in main or subsequent/nested function calls) is to use "Get-Variable" on "MyInvocation"...
# Get the MyInvocation variable at script level
# Can be done anywhere within a script
$ScriptInvocation = (Get-Variable MyInvocation -Scope Script).Value
# Get the full path to the script
$ScriptPath = $ScriptInvocation.MyCommand.Path
# Get the directory of the script
$ScriptDirectory = Split-Path $ScriptPath
# Get the script name
# Yes, could get via Split-Path, but this is "simpler" since this is the default return value
$ScriptName = $ScriptInvocation.MyCommand.Name
# Get the invocation path (relative to $PWD)
# @GregMac, this addresses your second point
$InvocationPath = ScriptInvocation.InvocationName
So, you can get the same info as $PSCommandPath, but a whole lot more in the deal. Not sure, but it looks like "Get-Variable" was not available until PS3 so not a lot of help for really old (not updated) systems.
There are also some interesting aspects when using "-Scope" as you can backtrack to get the names, etc. of the calling function(s). 0=current, 1=parent, etc.
Hope this is somewhat helpful.
Ref, https://learn.microsoft.com/en-us/powershell/module/microsoft.powershell.utility/get-variable