Sorry about the grammar mistakes, I'm not that bad!
That's not wrong at all. Childbirth is such a transformative, intimate thing. My husband and I also decided that we wanted to be alone until we were ready for visitors. With the exception of the birth team of course. In your case since you're totally alone, I'd recommend hiring a doula who can support you through the birthing process. Studies show that birthing with doulas make for much smoother deliveries.
Sounds very selfish to me. Especially when you would be moving in with them afterwards.
You are the mama and have the right to call the shots. If this time alone is important to you than you have every right to create a birth plan accordingly. I would broach the subject with your parents in an open and honest way. You can communicate how important they are, and how much you look forward to having them in your son's life. Let them know that you have put a lot of thought into it, and mentally you need this small amount of time alone to bond with your son. Assure them that you will have them on speed dial, and will keep them updated. Be honest about your feelings, and ask for some grace. Sure they might be temporarily disappointed, but once they do lay eyes on your precious child I am sure all will be forgiven. As you know, not all birth plans work out the way we envision. If you need some last minute support, give them a call, or have a friend on standby. I will you and your baby the best.