Even a stranger would become concerned if a well established pattern of contact was broken...it could save a life or at least help someone in need.
http://www.kplctv.com/Global/story.asp?S=14079358
I doubt the daughter's reaction would have been the same had she been in need, hoping someone would find her.
IMO this could have all been avoided with the daughter sending a text/email or call from another phone to her mother.
Screaming hateful things at anyone is not the best way to resolve an issue.
The daughter is an adult and is responsible for behaving like an adult regardless of how anyone treats her.
OP, calling her work numerous times was probably overkill but I don't think it's anything to beat yourself up over either. If I had to pick the "lesser offense" between:
A) Calling someone's work multiple times because you haven't heard from them and are overly worried- maybe for nothing or,
B) Telling your mother you hate her because she called your work multiple times looking for you.
It really isn't an unclear choice is it? At least I don't think so, then again everyone has different opinions on these things.
I guess if it were me, I would wait to talk to her until she calms down and then sit down together and set some clear boundaries regarding what is and is not acceptable in dealing with each other- especially in regards to calling each others' work as well as saying "I hate you"