to "send someone home" means to tell that person to go
home...
remember the term "send someone off"? you're not going with them
are you? 
what she is trying to say is that you "fetch her home", "accompany
her home", "escort her home", "bring her to her home", "drive her
to her home"...
the whole of singapore is using the wrong words.. and they don't
know it...