The Parents

I have several possibilities for why the parents want to keep her alive:

1) They don't believe in any sort of euthanasia for anyone whether they want it or not.
2) They are delusional and believe that there daughter is not “brain dead” and can get better. You can see this in their reading of her “smiles”, “laughs” and blinking that she does reflexively.
3) They are lonely old people and like all the media attention and support they are getting for their cause.
4) They believe their religion is the right one and everyone should adhere to it.
5) They never liked the fact that their daughter left them and now want to keep their baby for the rest of her life.

There are five believable reasons right off the top of my head.

You and the right wing are trying to make her husband out to be Scott Peterson or O.J Simpson. This happened 15 years ago, maybe it is torturous for him and his children to see his wife this way. There are plenty of non-capricious reasons for him to want to move on.