I dont think it is an unreasonable request especially when you are a first time mum and want to get to know the little person you created all on your own before having them overwhelmed with family.
I didnt want anyone to know when I was in labour- I hated the thought of everyone waiting around for me to have the baby, it felt like way too much pressure.
I will probably only have mum and dad to visit at the hospital this time because they will have our DD, and I want to see her as soon as possible, but everyone else can wait till I get home, as I will only be in hospital for 24 hours TOPS.