PS cmd to see if a Specific IE Certificate is Installed on a Remote Computer

Try it with this first, this will output the certificate list in a GUI table. You can check how the one you want to look for actually appears.
Then replace the Out-GridView at the end with the Where-clause of your choice.

Invoke-Command -ComputerName RemoteComputer -ScriptBlock {
	$Pattern = '\A.*?=\s*(?:"(?<Name>.*?)"|(?<Name>[^"].*?))\s*(,.*|\Z)'
	Get-ChildItem CERT:\ -Recurse |
		Where-Object {-not $_.PSIsContainer} |
		Select-Object PSPath, FriendlyName, @{n='IssuedTo'; e={$_.Subject -replace $Pattern, '${Name}'}}, @{n='IssuedBy'; e={$_.Issuer -replace $Pattern, '${Name}'}}, Subject
} | Out-GridView

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oBdA, thanks for the script, after configuring WinRM on the test computer and first running this script, I got the error message below:

The system cannot open the device or file specified.
    + CategoryInfo          : NotSpecified: (:) [Get-ChildItem], CryptographicException
    + FullyQualifiedErrorId : System.Security.Cryptography.CryptographicException,Microsoft.PowerShell.Commands.GetChi
   ldItemCommand
    + PSComputerName        : TestComputer

After changing this "Get-ChildItem CERT:\ -Recurse"
To this: Get-ChildItem -Path Cert:\LocalMachine\TrustedPublisher -Recurse

I now get the TrustedPublisher certs displayed. What do I need to replace "TrustedPublisher" with in order to get "Trusted Root Certification Authorities" displayed?

Ok I replaced "Cert:\LocalMachine\TrustedPublisher " with "Cert:\LocalMachine\CA" and I now can display some of the "Trusted Root Certification Authorities"  certificates, but not all of them. Any reason this would not list all certs in "Trusted Root Certification Authorities"?

Because "CA" are the intermediate CAs.
Try Cert:\LocalMachine\Root, or just Cert:\LocalMachine.

Cert:\LocalMachine displays a lot more certs, but still not able the see the specific certs I'm looking for. When I look at the specific certificate in Internet Explorer > Internet options, the "Friendly Name" column shows <None>.  If I change "Select-Object PSPath, FriendlyName"  TO "Select-Object PSPath, IssuedTO" the scripts errors.

oBdA - If it's not already then could you please update your script to query for "IssuedTO" instead of the FriendlyName?

It already does that, that's what the calculated property is for.
Use it exactly as posted (except for the computer name, obviously), and use Out-GridView's integrated filter to find the certificate you're looking for.

Invoke-Command -ComputerName RemoteComputer -ScriptBlock {
	$Pattern = '\A.*?=\s*(?:"(?<Name>.*?)"|(?<Name>[^"].*?))\s*(,.*|\Z)'
	Get-ChildItem CERT:\LocalMachine -Recurse |
		Where-Object {-not $_.PSIsContainer} |
		Select-Object PSPath, FriendlyName, @{n='IssuedTo'; e={$_.Subject -replace $Pattern, '${Name}'}}, @{n='IssuedBy'; e={$_.Issuer -replace $Pattern, '${Name}'}}, Subject
} | Out-GridView

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Ok that works, the cert name I was looking for is actually displayed in the "Subject" field instead of the "Issued to" field the way it is shown in Internet options > Contents > Certificates. Instead of having to run a script for each machine I want to check and filtering the output, is there just a one line PS command to remotely show me if that cert exist on a remote computer?