I had a miscarriage at 9 weeks with my first child, and had told everyone around us. It was hard enough to deal with the miscarriage, but to deal with telling everyone who kept asking how I was feeling, why I wasn't showing, etc., was horrible. We decided from then on to wait until 3 months, which most doctors advise, anyways, to tell anyone we were pregnant. We rejoiced, worried, and did all the normal things, in our own home, but the rest just wasn't public! We have 3 healthy boys, and saved myself alot of angst by telling people too early.
I know your situation is different, but your baby will never know you didn't tell people right away. You are waiting for all of the right reasons, to protect others you care about. The baby will feel your love and excitement, and will grow and develop to feel loved, regardless of when you announce the pregnancy to family!
Best wishes for a happy, healthy 3rd child! Our third added such craziness (happy craziness) to our lives!