I wonder if she means she like it at home , is she happy , plays okay , no other symptoms she is upset.Could it be a habit she has got in to because it got her attention, try saying nothing about it, so when she says it, ignore it or just say we are home and distract her with a game .
I used to say this, a lot. But, I was in my teens. I used to tell my dad, I wish I could be at home. For me, even though I was home, I didn't feel AT HOME. It was a combination of things. I wasn't at home with myself, didn't feel comfortable with myself. I felt alone even when I wasn't. I don't know if a three year old can feel things like this. But, it was a comfort thing for me.
If it where my child, I would be asking a psychiatrist or psychologist. One who specializes in children. It is a little curious. I wouldn't worry about it too much, but I would be very curious and wanting to know how I can help my child feel at home when she's at home.
I would keep a journal of everything that is happening when she says it. Time, date, moods and anything else to see if there is any kind of pattern. My 2 year old sees dead people, or she's got an over active imagination that allows her to know things before they happen and names of dead relatives that I didn't know we had. It scares me too. If Silva Brown wasn't so dang expensive I would take her to her. Perhaps as your daughter grows she will be able to explain it. Have you asked a child psychologist? Good luck keep me updated.
I would ask her to describe what "home" looks like. I have been "in tune" (hate the other term), since birth or as far back as I can remember (age 2). I would say that if she describes what most would call "heaven" then she is longing for the peace she "feels" there. I too used to say "I want to go home"..and still do to this day, on occasion. I wouldn't automatically think that she is say she wants to "die", just the stress is getting to her and she ~needs~ to feel more relaxed and peaceful. Children have a knack of picking up on other people's stresses and worries..so if you can relax a bit too it'd help her to relax.
I have watched Sylvia go down hill in her career. When you charge money, not donations, you will loose your "gifts". I have seen this time and time again..not just with Sylvia. I'd find someone that ~doesn't~ charge..they will/should be more reliable. ;)