Hi there, congrats on your wife pregnancy.
Ya, there is no diff for foreigner to see gynae at private or public hosp like KKH but i would suggest you to apply LTVP for your wife and she confirm will get LTVP+ since she is pregnant and do not forget to "check" the box tat asking whther is your wife pregnant on the application form. And do not forget to bring along the EDD cert when attending the formality.
and yes, if you choose to go KKH, you wife is under private rate and can only choose either class A1 ward or B1 ward with foreigner rate. but once u get LTVP+, you will get some subsidize rate like PR for the gynae visiting fees and the delivery package/charge will follow PR rate too (but still, u can only choose either class A1 (single bed) or B1 (4 bedded).
you may PM me if u wan to know more coz my wife is holding LTVP b4 pregnant and i quickly renew her pass again once get to know she is pregnant and she got the LTVP+.
cheers.