A story stretched too far?

I'm a good chunk into a book.  It's an okay read, but I've been having problems with the believability of some of elements of the plot in what is meant to be a realist piece of crime fiction.  That's fine, I can live with plot devices if they're not too clunky or stretch things too far.  However, last night I reached a point where the believability got stretched to, what seemed to me, breaking point.  Here's a brief summary of events:

An abusive husband is stabbed whilst out walking.

His wife’s alibi is that she was visiting a back-street abortionist the evening he was killed.

Her teenage daughter corroborates her story, but the abortionist (who would have been committing a crime herself) doesn’t.

The wife’s mother was convicted of killing her husband in the same fashion.

There is no material or forensic evidence (no weapon, no clothes with the victim's blood on, etc) and no witnesses to the stabbing.

The police charge the wife with murder on the basis she'd been heard to threaten taking revenge for her beatings and her alibi only being supported by her daughter.

Would the police really charge her with murder on the basis of a contested alibi and a supposition that murder runs in the blood, when there is no hard evidence or witnesses?  On what basis are they going to convict her other than loose conjecture?  Would it even last two minutes in a court of law?  Does this sound reasonable or far-fetched to you?  I'm going to soldier on, but my faith in the story has been undermined for now.