This is typical of Microsoft. I can make life easier for you by explaining a few things
1) Microsoft manage the entire install process. No Visual Micro code runs during install
2) Visual Micro produces a VSIX file that Microsoft installs.
3) A VSIX file is actually just a zip that you can open.
4) The only way to tell Microsoft what an extension needs is to add it to the manifest text file that you will see in the VSIX.
5) All Visual Micro needs is for C++ to be installed. If you have not installed the C++ module then Microsoft will attempt to install it.
6) I don't see any Visual Micro stuff in your installer trace. I do see a lot of extensions and modules that Visual Studio is not entirely happy with and that indicates the Visual Studio installer is attempting to complete installation of other partially installed software.
We can see in your trace file that redgate is attempting to install something and I think the above shows how we can be sure it is unrelated to Visual Micro.
Sorry it's a pain. I suggest asking redgate what has happened. Keep in mind that some software runs via a normal installer but attempts to install VS extensions at the same time. I would check you Control Panel > Add or remove programs. Also keep in mind that Visual Studio will only install one package at a time.
I am happy to take any direction from Microsoft but I can't see there is much room for error on Visual Micro's part.
04/07/2018 15:52:45 - Package 'Redgate.SQLPrompt.VsPackage,version=8.2.5.2924' failed to install. System.IO.IOException: The file 'C:\Program Files (x86)\Microsoft Visual d.Net20.dll' already exists.
at tall|28_1(PackagePart part, Boolean saveExtensionManifest, <>c__DisplayClass28_0& , <>c__DisplayClass28_1& , <>c__DisplayClass28_2& , <>c__DisplayClass28_3& , <>c__DisplayClass28_4& )
at Microsoft.VisualStudio.Setup.Installer.VsixInstaller.InstallCoreInternal(String localPath, String installDir, InstallablePackage pkg)
at llCore>b__0()
at Microsoft.VisualStudio.Setup.Installer.FileInstaller.DoAction(Func`1 action)
at Microsoft.VisualStudio.Setup.Installer.FileInstaller.InstallCore(String localPath, String installDir, InstallablePackage pkg)
at Microsoft.VisualStudio.Setup.Installer.InstallerBase.InstallHelper(InstallData installData)
04/07/2018 15:52:45 - Skipping cache of package 'Component.Redgate.SQLPrompt.VsPackage,version=8.2.5.2924' since the package or a parent package had a vital failure.
04/07/2018 15:53:04 - Install Error : Microsoft.VisualStudio.Setup.PackageFailureException: Package 'Redgate.SQLPrompt.VsPackage' failed to install
at Microsoft.VisualStudio.Setup.InstallOperation.Run(CancellationToken token)
at Microsoft.VisualStudio.Setup.Engine.RunOperation(InstallOperation installOperation, CancellationToken token, ExecuteAction action, ITelemetryOperation telemetryOperation)
at Microsoft.VisualStudio.Setup.Engine.RunCoreOperation(InstallOperation coreOperation, ExecuteAction action, ITelemetryOperation telemetryOperation, CancellationToken token)
at Microsoft.VisualStudio.Setup.Engine.Install(Product product, String destination, CancellationToken token)
at stall(InstallableExtensionImpl extension, Boolean installPerMachine, Boolean isPackComponent, IDictionary`2 extensionsInstalledSoFar, List`1 extensionsUninstalledSoFar, IInstalledExtensionList modifiedInstalledExtensionsList, IProgress`1 progress, InstallFlags installFlags, AsyncOperation asyncOp, Version targetedVsVersion, IInstalledExtension& newExtension)
at allableExtensionImpl extension, InstallFlags installFlags, IDictionary`2 extensionsInstalledSoFar, List`1 extensionsUninstalledSoFar, IInstalledExtensionList modifiedInstalledExtensionsList, AsyncOperation asyncOp, IProgress`1 progress, Version targetedVsVersion)
at lableExtension installableExtension, InstallFlags installFlags, AsyncOperation asyncOp, Version targetedVsVersion)
at llableExtension extension, InstallFlags installFlags, AsyncOperation asyncOp)