"So my network is using sites.ABCXYZ.com I've setup a sub site which is sites.ABCXYZ.com/sitename" -- this can work, I've done it.
You want sites.abcxyz.com as an actual subdomain, created in CPanel or whatever tool your account uses.
Then configure WordPress as Multi-Site in SubFolder mode (not subDomain mode, you can't do subdomain of a subdomain).
Then otherdomain.com has to be an Add-on domain, not a Parked domain. It has to be configured at the server level to go to sites.abcxyz.com and then WordPress will take things from there.
You must have have wildcard DNS working, so WordPress can get all those "virtual subdomains" working.
Then you need the Domain Mapping plugin set up correctly and configured correctly, and the individual site mapped correctly. I cover all of this Domain Mapping plugin setup and configuration.