Hey, really sorry about the delay. A coworker had emailed Yahoo! to try to get some documentation on doing this, since it is supposed to be possible in your control panel. I checked back in with him, and he said there is no documentation per se, but that people who don't see the option in their account can call Yahoo! and they will set it up. He was also going to send me the number to call, but I have not gotten it yet. I will check with him today about the number.
I can imagine your frustration about this being such a long process, and I would feel the same if I were you. When I get the number, I will go over the steps with him again, and I will also see if there is any way to confirm this info with Yahoo as well.
**EDIT***
Meanwhile, I see that both domains are on Yahoo nameservers, but safeandcozypets.com doesn't have a CNAME record, while your other domain, safeandcozypet.com, does have the CNAME record entries (without quotes):
"www.safeandcozypet.com" CNAME stores.yahoo.net.
stores.yahoo.net CNAME html.store.yahoo7.akadns.net.
Im not sure you need both of those in there - it would seem you would only need the first one. In either case, you can try the instructions here:
Advanced DNS Settings
Specifically, the 'How do I set a CNAME record" link:
How do I set a CNAME record? - Yahoo! Small Business Help
Advanced DNS records like these typically take 2-3 hours for you to see the changes. Try adding the first, wait a day, then try the second.
Finally, you may also need the A record like your other domain has - check that for the one that's working, and copy the info and check to see it the one that's not working has it or not.
As I said, I will still get that number for you and post here when I do.
Good luck