Hi V. R:
Allow me to preface what I am about to say with; I am a medically retired Physician Assistant Certified in both PA & AK, I am also a certified Midwife.
I am hoping that this explanation will help you a bit.
There are several different formations of the hymen, some more common than others.
In about 1 in 2000 females, the hymen fails to develop any opening at all. This is called an imperforate hymen and if it does not spontaneously resolve itself before puberty a physician will need to make a hole in the hymen to allow menstrual fluids to escape. A hymenotomy may also be required if the hymen is particularly thick or inelastic as it may interfere with sexual intercourse.
Most common forms of the hymen:
When considering the shape of the hymen one must be examining the patient in the prone position on their back with 12 O'clock being on top by the belly and 6 O'clock being inline with the anus.
Crescent-shaped, crescentic, or posterior rim: no hymenal tissue at the 12 o'clock position; narrow band of tissue starts at 1 or 2 o'clock going clockwise, is at its widest around 6 o'clock, and tapers off at 10 or 11 o'clock
annular, or
Circumferential: the hymen forms a ring around the vaginal opening; especially common in newborns
redundant; sometimes sleeve-like: folds in on itself, which sometimes causes it to protrude; most common in infancy and at/following puberty due to estrogen levels; can be combined with other type such as "annular and redundant"
Less common forms:
Fimbriated, or denticular: an irregular edge to the hymenal
orifice; more likely at an age when estrogen is present
Septate: the hymen has one or more bands extending across the opening
Cribriform, or microperforate: the hymen stretches completely across the vaginal opening, but is perforated with several holes labial, or vertical: hymen has an opening from the 12 to the 6 o'clock positions and can look similar to a third set of vulvar lips
Imperforate: hymen completely covers vaginal orifice; will require minor surgery if it has not corrected itself by puberty to allow menstrual fluids to escape
I realize that there are seems to be a lot of medical mumbo jumbo here, hopefully it has explained your daughters condition to you. Although rare, it is rarely permanent.
To put it in really simple terms, she will out grow it, and if she does not, then the things required to fix it are very simple and have very few risks attached.
I hope that I have been of some help to you.
As far as the mother who answered you with "get a better Doctor"; Your doctor is doing just fine, if you feel more comfortable with a second opinion then of course you should get one.
God Bless,
J.