There is **no way** to make this work. If you *own* both domains, obviously you can redirect one to the other. At that point, however, it is no longer “multiple websites” – it’s *one* website that has several domain names pointing to it.
> I have subdomain like so subdomain.website.com I want to hide the parent directory from the URL
There is no “parent directory” (no “directory” at all) in that URL. If you meant something else, perhaps you could explain further.
@NSR – I’m glad you are choosing to purchase the domains because hacky attempts at changing the URL are never a good idea as far as I’m concerned. To anyone who notices the hacky nature of the URL, its a red flag. I’ve seen hacky URL stuff kill SEO and as you pointed out, usability can be impacted.