Hi! We moved to Lamma last year - so I can answer any questions you can have, but I'll address those you've discussed first:
1) there are not many official playgroups here (there is a lot for older children, though) but the Lamma church has a playgroup called "the hangout" on back street (the path to HSY beach) and Banyan offers Mommy and Me classes 1-2 times a week (
http://www.banyanhouse.com.hk/Banyan_House/Parent_&_Child.html) and the community is fantastic. Superb. Amazing. I LOVE Lamma.
2)emergencies: there is a clinic that has a nurse on call 24 hours. in a true emergency you are airlifted to Pamela Youde or taken by police boat to Kennedy town and ambulanced to Queen Mary.
the only real downside to lamma is bugs. because it is "remote" (though no farther than DBay...) I have yet to find an exterminator willing to come here and there is sort of a live with it mentality... we have now managed to keep all critters out for a fair amount of time.
I am happy to answer any questions you have, and if you do decide to move here I can introduce you to some other mums with little ones, and I am sure you will soon meet more! Lamma is like a small town in the middle of Hong Kong. We have considered moving back to the US but we really do LOVE it here.
I also suggest Jackson over the other property agents as he was able to find what we wanted even with a very limited number of available units on Lamma. Bear in mind everything is very local, so you will put in some elbow grease, but nowhere we have lived in HK up to now has felt so much like "home"
oh and education I can't really speak to - we send my older girl to Banyan for Kindy and will likely leave HK before she hits primary as we are not interested in the school system here, but many kids take the ferry to kennedy and bradbury and other schools daily.