Dreamweaver CS6

If the old copy of DW is yours it was probably tied to an old computer. The program will only add installations if you install on a new computer, or you update or change hardware of your existing computer. Installing Acrobat would have no effect on the DW license. If you do not have access to the old computers to deactivate them, unfortunately you will not have any available options to you as Adobe stopped resetting activation counts as of the first of this year as most of the CS6 apps no longer run on a modern OS and the software has been unsupported. To be honest at this point, DW is in minimal maintenance mode and you may be better off looking for an alternative editor based on your workflow.

Which operating system?

How many users are on this computer?

I can't see how installing Acrobat alongside legacy Creative Suite 6 would cause your installed software to disappear.  That makes no sense. Software doesn't just vanish unless someone manually removed it.

Ensure that you're logged-in to your computer with the same computer profile that had access to CS6. You may need to contact your IT dept for assistance.

See if anything here helps you, this is the most current info from Adobe themselves: https://community.adobe.com/t5/download-install-discussions/activation-limit-reached-for-non-subscription-adobe-desktop-applications/td-p/14804413/redirect_from_archived_page/true

If you can't get up and running there, I'm pretty sure you'd just be out of luck. Adobe has moved DW to a minimum maintenance mode, they're no longer doing any kind of updates/new features other than OS compatibility, security and third party library patches.