@D81
Okay,
I have some time to post findings. In the documentation, it states that whether using a single virtual machine for the database and manager, or using separate virtual machines for the database and manager, to utilize the Windows Integrated Authentication. When selecting this option in the installation of App Volumes, it specifies that it will "automatically use this server's SYSTEM account" of the local machine where App Volumes is being installed. And this is the issue.
A computer object and its SYSTEM account cannot be added to an SQL database and given permissions (at least not to my knowledge), and only user accounts can (whether it's an SA login that is created within the SQL database or an Active Directory Windows authenticated login). Therefore, App Volumes attempting to use the local machines SYSTEM account will fail every time unless there is a way to add another machine's SYSTEM account to the SQL database and give it permissions, which again, I have not found a way to do so and there is no documentation from Omnissa/VMware on how to do so either.
The resolution is actually quite simple, it's just not anywhere in the documentation. If you plan to utilize two virtual machines and separate the database from the app volume manager, you need to login to the database virtual machine, open SQL Server Management Studio and connect to the database, right-click on the database and go to Properties, in the properties window, click on Security, and then change it from Windows Authentication Mode to SQL Server and Windows Authentication Mode and then click OK.
Ensure that your SA account is enabled for login by expanding Security > Logins on the left hand side, right-click the SA account and go to properties. In the Properties window, click Status and change login from Disabled to Enabled and click OK. You can create a secondary SA account with less permissions to the databases and only give what is necessary for App Volumes if you want to stay a little more secure on the database side of the implementation.
Now, when you run the App Volume installer, and get to the section of choosing your remote database server, select the radio button for "Server authentication using the Login ID and password below" and supply the SA credentials. Uncheck the box for "Enable SQL Server certificate validation" and proceed with the rest of the installation to your desired settings and it should successfully install.
@D81, I included screenshots as I'm personally a visual learner and know others would additionally benefit from screenshots. Please let me know if you run into any additional issues or if it is successful for you. I would like to know if my method works for others.
@Jeff Ulatoski, would not mind syncing up with you and discussing further on this and the product overall as a whole. I have even thought about making an instructional YouTube video to specifically show this method for installation to better help administrators and engineers but would need some temporary licenses to be able to create the videos and show the process.
Levi Hayes's post in AppVol Manager Can't Generate Self-Signed Certificate was marked as the answer