How can another domain completely conceal all traces to primary domain?

Hello there, English isn"t my first language, so please excuse any mistakes, if there has any part need me to describe again, please ask me. I have a VPS package, I can login my WHM and have root privileges. I have two domains running on the VPS, for examples, example1.net & example2.net. example1.net is the primary domain of my account, it using a dedicated IP. The two domains run two different sites, they shared some same database and folders, that is what why I put them in a same WHM account. I want example2.net to act as a complete independent entity, revealing no traces to example1.net under any circumstance: They do not have any connection, whether it is for domains or IPs from any tools. Or the original record from the headers of emails. To do those, I bought another dedicated IP to assigned to example2.net when necessary. I think when they have different dedicated IP, then regardless of any external inquiry, the two domains should be not appear in the same query results. But when I tried two different ways, it did not work: [LIST]

I tried the "addon domain" way to addon example2.net and assign a different dedicated IP to it, and then query example2.net on some tool, it showed "server.example1.net" in the results. And in the two ways, emails sent from example2.net, the gmail recipient will see someone@example2.net "via server.example1.net" in the email and "example1.net" in the message headers of the email. e.g. Message headers - Gmail Help How to do for that? Thank you!