Masking CNAME/A Record Requirements from Clients
Solution 1:
Start by using proper terminology. I don't care what anybody else says or thinks but there is no such thing as a vanity domain or a vanity name server. There are domains and there are name servers. You may choose to call them "vanity" as a cheeky marketing ploy but you're only serving to confuse your customers more by calling them something that has no root in technical accuracy.
It doesn't sound like you have the requisite technical knowledge to be managing the name servers for your customers so I would advise you no to.
I work for a client that hosts email for a large number of customers. This client does not host the DNS for these customers. This client advises their customers on what DNS records to create/change and assists them in doing so if needed. If you are not in the business of providing rock solid, fault tolerant DNS then you shouldn't be doing so.
I see this all of the time. Someone hosts a VPS, or a web site, or email for a domain and they think they should/need to host the DNS for the domain. They don't have the technical know-how or the appropriate infrastructure for doing so and the next thing you know, a customer's public presence (email, web, etc.) is unavailable because something's wrong with their DNS, because someone who has no business hosting DNS is hosting it and has fouled it up.