Killing children is not a constitutional right. There is a right to life though.
This is the sticking point. First, I'm not pro-abortion, but I don't have a closed mind about when human life begins either.
Until we, as a people, can agree on when a fetus becomes an unborn child we are stuck at a standstill.
I posit, as a compromise, 20 weeks (5 months) is when the neurological system enables the fetus to feel pain. To feel pain the brain must be developed enough. This 'could' be the moment the fetus becomes an unborn baby (or child as you say).
If the pro-life side is stuck on the moment of conception; this issue will never find a compromise. If the pro-abortion side is stuck on 'up to the moment of birth'; that won't work either.
I know this is an emotional and passionate issue for some people. Heck; it's the only issue that matters for some folks. Without a compromise and both sides saying all or nothing; we might as well hang this issue on the clothesline and forget about it because nothing will happen going forward.