Try as hard as I may to understand – do babies have Constitutional Rights, or not?

Scott Peterson is currently on death row because he killed his pregnant wife, Laci, and their unborn child, Connor.  He was charged with two murders, not one, and this type of punishment happens in other cases and states too.

I understand that people can be punished for killing an unborn baby, but only if it is a crime that the mother doesn’t choose.  But for the life of me I can’t seem to wrap my head around the fact that the same crime is acceptable if the mother chooses to kill her own child, and a doctor participates, after he has taken an oath to protect life. How is the doctor any different than the criminal murderer?  Should a doctor lose their license by going against the oath that they took to protect life? Why do people who aid in a murder also held responsible, so how is the mother different than a criminal who aids in a murder?  (LET ME STRONGLY SAY THAT WE NEED TO HAVE EMPATHY AND COMPASSION FOR MOTHERS WHO FEEL THEY HAVE NO OTHER CHOICES BECAUSE THEY DO NOT HAVE THE SUPPORT OR EDUCATION TO LET THEM KNOW THERE ARE OTHER OPTIONS AND PEOPLE IN THE PRO-LIFE COMMUNITY THAT ARE HERE TO HELP THEM.)

In the Peterson case, baby Connor was given Constitutional Rights, but when it comes to abortion, the baby doesn’t have Constitutional Rights.  Aren’t Constitutional Rights suppose to cover ALL people?  According to the United States Declaration of Independence – “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are LIFE, Liberty and the pursuit of Happiness. ——”