I'm really not too sure about Native American sumbols for birth (or for any culture really), however I DO know that the totem animal for birth is a hippopotamus. Coincidentally, every time dc sees a picture of one dc yells "MOMMA!" with glee and points (
: still not sure how I feel about that LOL)! I'm really not sure how you feel about tattooing a hippo onto you (and really, you could go with more pretty comical hippos like from the Fantasia movie, or realistic ones, or even have a custom tribal hippo head done or something like that). The totem link is here:http://www.crystal-cure.com/protection-hippo.html
Perhaps you could tattoo a tree of life with a butterfly on/near it for each daughter (a butterfly is a well-known symbol of birth and change). Each butterfly could be in a different colour to represent each of your daughters unique characteristics (colour meanings can be found by doing a simple google or yahoo search). The actual tree could be your own birth tree (try http://www.geocities.com/SoHo/Cafe/8021/trees.htm
to find out your birth tree).
A more traditional birth symbol (according to Sheila Kitzinger) which has been used in different cultures around the world for centuries in art and textiles etc can be found at: http://www.everyday-miracles.com/logo.htm
. It's quite beautiful, maybe you could have the butterfly concept somehow incorporated into it.
Good luck with whatever you choose. I know a positive birth experience is a life-changing event and I can definately understand your decision to commemorate it by visually adding it to your skin.