No doctor would dare perform an abortion on Michael Corleone's wife
.
Probably not. Though abortion was illegal in the US at that time, any woman or girl with a few hundred dollars (probably less than $500) could have had an abortion done by a real doctor in an office or clinic. Still, it was a risky business for a doctor, even in Nevada; and although Michael was trying to pose as "legitimate," a Dr. would have to be deaf, dumb and blind not to know his reputation. That's why I tend to think it really was a miscarriage, as Tom said, not an abortion.
I agree that it would have been difficult or impossible for Kay to get an abortion in Nevada.
But there are early versions of the GFII screenplay floating around the web that include a subplot where Kay escapes the compound while Michael is in Cuba and briefly returns home to New Hampshire. I think Kay could have found a willing doctor (maybe a family friend) there who would have performed the abortion.
As for the divorce/custody issue, I can't imagine any circumstance in which Michael would have allowed his personal business to have been aired in public court. I think the arrangement they appeared to have in GFII - Kay leaves the kids with Michael but has visitation rights - was worked out privately.
