In a very unequivocal teshuvah (1:894), Rav Moshe Shternbuch says that one should not induce labor “chas veshalom.” Hashem has scheduled the baby to come out exactly at the right time and it should not be influenced by a doctor’s schedule. The additional time may help the baby complete development of its body or mind. Additionally, the baby’s mazel is dependent on its coming out at the appropriate time.
Rav Shternbuch says in the name of the Arizal that one should not write a kemeiya for a woman to speed childbirth, because it can alter the baby’s mazel and cause it a life of poverty, pain and early death., r”l.
He quotes the Igros Moshe (Yoreh Deah 2:74) who says that all childbirth is life threatening. Although bringing yourself into a life threatening situation is not permitted, since it is the nature of the world, it is permitted for a woman to conceive. However, to induce labor before the natural time is tampering with nature and it is prohibited to put yourself in this dangerous predicament.
If the doctor says that it is dangerous to the mother or the baby to wait, then it is certainly permitted to take the baby out by any means. The above discussion applies to situations where that is not the case.