Don't call me ...

don't call me that!

not "like that."

... and in case 'he' calls 'her' 'Baby' and she dislikes it, she may reply:

'Don't you babe me' . . .

@ Daddy

I heard that before. Can you give me some more examples for don't ... me!

http://books.google.com/books?id=t53-tYF3ml8C...
Fern Michaels, Plain Jane, pg. 55:
I don't think he would say 'lick me' to anyone. Where did you hear something like that? I'm taking it out, sugar." "Don't you sugar me, Fred McGuire!"

http://www.cassandrakane.com/escapes-antholog...
Sark’s lips quirked. “All alone, baby.” “Don't you baby me,” she said coldly. “You and I are over. Were over,” she corrected, “the minute you stepped out the door.”

http://www.fanfiction.net/s/4985957/1/Arguing
"Honey, it's not polite to interrupt a conversation," Cal raised his eyebrows and pointed his index finger at her, making her feel like a small child [...] "Oh don't you honey me, I know what you're thinking," Gillian glared at him; she wondered how much longer she would have to do this.

Examples.

@ Nina, re #4: Sorry, no! - However, where the original can be found, maybe there are others:

http://www.google.de/search?hl=de&rlz=1W1DVXE... . . .

... und die weit offene Suche hier:

http://www.google.de/search?hl=de&rlz=1W1DVXE... . . . ;-)