I'm sorry. Not for you, but for her.
Now, I do think that when I hear two people going on and on, loudly, in a public place, swooning over each other, having some kind of contest about who can come up with the smoochiest nickname, licking each other's earlobes, making out with no regard for others around them, etc., that sometimes can be a bit much. Not to the point of vomiting, however.
However, to greet one's immediate family with a cheerful greeting, to carry on a brief conversation, sounds very nice. Saccharine? Vomit? I think she's just wishing she had someone who cared about her welfare like your family does. The problem lies with her, not you.
I would not excuse myself, justify my actions or change anything, if I were you. It sounds like you are not taking up office time for a personal phone call, not jumping on your desk like like Tom Cruise jumped on Oprah's couch and shouting "I love this person!" or making annoying kissing noises on the phone in a business setting.
I would continue to demonstrate love to my family, and send a positive thought or prayer to this woman who is so unloved that overhearing a cheerful greeting makes her want to vomit. And I want to encourage you to keep making those brief but reassuring phone calls.
No, wait...next time you're at work, instead of saying "good morning sweetheart", why don't you sing, in your most lovely lilting voice, the song from Sleeping Beauty (I know you, I waltzed with you once upon a dream) or some other sweet Disney song! (just kidding. you might have to supply her with an actual airplane barf bag if you did that!)