I need to create the CNAME record:
abc.xyz.mydomain.com = verify.azure.com
but my DNS provider (www.freeparking.com) only allows me to create it at the sub-domain level (i.e. xyz.mydomain.com). I have confirmed with the technical support that the cannot create a CNAME at the sub-sub-domain level (i.e. abc.xyz.mydomain.com).
Is there a way I can create a sub-sub-domain level (i.e. abc.xyz.mydomain.com) CNAME record by referencing DNS names? If not, what is the best solution?
Your question lacks technical rigor, probably due to a lack of knowledge about how DNS works, so I am going to assume you mean the following:
If this is correct, get a better hosting provider; zoneedit.com, for example, is free and allows you to do anything that is valid in a DNS zone.
By sub-sub domain I assume you mean x.y.domain.com. And by freeparking.com not supporting it I assume you mean their DNS management system doesn't allow you to add x.y as a CNAME record.
I think you will need to switch domain providers, or use a different nameserver, since Azure will surely be looking at the authoratitive name server for authentication.
Are you sure that Azure require you to register a sub-sub domain for authentication?