I wonder if she's saying these things, not because she wants a different living situation, but because she's three.
My three year-old DD says stuff like this all the time. My 5 yo DS went through a phase like it two years ago. They were testing, basically, trying to see if I'd soften up, or if their dad would. We spent a lot of time saying things like "I'm sorry to hear that. Eat your vegetables."
Now and then, our kids stumble upon words that push our buttons HARD. In a lot of those cases, the kids have no idea what they're doing. Your daughter says she wants to go see daddy, and she means "I bet Daddy would let me!", but in the meantime, you're being hit with all kinds of guilt that your DD knows nothing about. It's really hard to remember to look at it from her child perspective, as opposed to your adult one, or even through an adult filter concerning her child perspective. Most of what children this age say is very in the moment - she's thinking about bedtime or the socks she hates or who has better popsicles, not about family structure or what's best for her in the long term.