I live in Tseung Kwan O and delivered two babies here (in 2010 and 2012) in United Christian (public hospital in Kwun Tong) so maybe can be of some help.
1. If you live in Hang Hau and want to go the public route, at least under the subsidized care system, the hospitals in your catchment area would be United Christian in Kwun Tong and I think Queen Elizabeth. Your check-ups would probably happen at the maternal and child care centre in Hang Hau largely conducted by midwives and, if there are even slight complications, at Tseung Kwan O hospitals. However, some women prefer to register at Pamela Nethersole in Chai Wan as it offers the option of a private room after delivery (only if available on the day you go into labour) and that hospital is not too fussed about where you live (unlike Queen Mary, which is quite strict about catchment area).
2. As a private paying patient, however, you could probably pick any public hospital and try to register as a private patient. For example, I know that in the private route at Queen Mary, one can see the same doctor right through till delivery, have a private room (for a comparable cost to being in the ward in other private hospitals etc.)
3. Your best bet would be to go down to the hospital as you may have discovered you have to be lucky to get someone helpful who will speak English on the phone if it's just an enquiry (if you're a patient, they are much more helpful... also you already know the system). Keep in mind that the rules about non-local mothers delivering in Hong Kong have changed. (
http://www.info.gov.hk/gia/general/201106/24/P201106240180.htm) However, it seems you can still book under a quota if you are lucky.
4. Union Hospital (private) in Sha Tin runs a polyclinic in Metrocity Po Lam, where you can see a private doctor for antenatal checks if you want one nearby. My friends recommended Dr Yu Kai-man. He is very experienced but also very busy. I used the polyclinic but saw a younger female doctor who no longer sits there because I needed to be able to make last minute appointments. I intended to deliver public so I wasn't very picky. However, if you are paying for delivery anyway, might as well have the same doc at delivery. I'm not sure how pro-vaginal delivery Dr Yu is but I think he should be ok. Sha Tin is actually not that far from Tseung Kwan O by cab...supposedly so that's an option for delivery.
5. For my second pregnancy I saw Dr Jimmy Mak at Baptist Hospital. I am pretty sure he will not push you into a c-section. He was supportive of my desire to have a vaginal delivery (I am against referring to this as a normal delivery) and when he realised my baby is breech, he explained all the options - ie ECV (baby is manually turned by a specialist), c-sec or vaginal breech delivery. He does not do the latter I think nor did I want one. He also is not qualified to do ECV but wrote me a letter to the public system requesting them to expedite my case and do one for me (which they arranged). He also showed me exercises I could do to help the baby turn. At no time did he try to push a c-sec. However, I did not actually end up delivering with him because I had to have an emergency c-sec and knew I wouldn't be able to afford the private cost of that so went public in the end. There are other threads on this site about him so you could check.
Baptist Hospital is in Kowloon Tong, however, and by MTR it might take not much longer than going to Central, so keep that in mind. For me, it was opposite my office.
Feel free to ping me if you have further questions and I'll try to help.
