What world is this, that Sara gets to act as lawyer in a case that involves her own family members? (On both sides, no less.) Is that even legal?
You're thinking of doctors, who are legally not allowed to operate on family members and friends. In the case of lawyers, it's ill advised but legal.
It's completely legal for a lawyer to represent a case involving family. Sara also has strong traits of narcissism, so she may think that such an important case will benefit from her involvement.
In relation to the first problem stated... I was going to add my bit, but I didn't want to make it longer, as this will open up a different set of issues: The edition this troper owned contained an interview with Jodi Picoult after the very end. One of the questions she was asked was why she chose to end it this way. Her answer? Because it was the most "medically realistic" ending according to a nurse she talked to. I could go into incessant ranting about this, but...yeah.
Saying it is medically realistic isn't fair. The nurse would obviously say that this would be the right ending because she would always be on the side of the one who is sick, not considering anyone's else feelings. Also, the nurse is breaking the whole idea of "do no harm" by suggesting such an idea.
I took "medically realistic" to mean that Picoult wanted Kate to survive, and the nurse agreed the only "medically realistic" way she would survive would be to get the transplant — so bye-bye, Anna, tough cookies. I can't imagine any scenario where "medically realistic" = "be rendered brain dead in a freak car accident minutes after becoming medically emancipated after which your guardian agrees to have your organs harvested without a second thought". I certainly wouldn't want to be a patient at a hospital with that definition of medical realism... Mind you, I suspect that section of the interview was mostly an exercise in passing the buck for the Deus Angst Machina / Debate and Switch.
I asked Picoult at an event, and she said something akin to you, like everyone else, took her for granted, so shame on you (not even joking). So theres a reason, at least thematically. It was a few years ago so I dont remember details.
At the start of the movie, the doctor who suggests Sara have a Designer Baby states that it's technically illegal. Why wasn't Anna taken away when she mentioned she was a Walking Transplant?
Perhaps they exploited a legal loophole, or it was an "open secret" at first — everyone knew why Anna was really born, but everyone was careful not to write it down in case it was used as proof. By the time of the court case, though, there's less justification. I suppose since there's a case already in motion that would prevent her being used as an organ factory, the legal system might have decided on one case at a time — perhaps Child Protection would have stepped in if Anna lost the case? This is one bit that I think the book did far better than the film; the doctor is put on the stand and grilled by Campbell, who demands to know why the hospital allowed dangerous, painful and invasive procedures on a patient when her best interests were not served by the procedures. It makes it clear the hospital had to bear some responsibility for suggesting that course of action in the first place... Of course, nothing ever comes of it, as far as we know.
As I understood it, having a Designer Baby is not illegal in itself but it is illegal for a doctor to suggest it.
Without getting into the can of mutated fire ants, it's not illegal for a doctor to suggest the idea (actually, the USA doesn't have any laws about "savior siblings"), so the way I took it was that they really meant that the Dr's suggestion violated the hospital code of conduct/ethics or a rule about giving referrals (something about liabilities).
How the hell did the parents in either the book or the movie even get to keep custody of their kids? One ends up a semi-psychotic pyromaniac out of neglect, and the other they treated like an organ bank? Especially the mother, they're just awful, AWFUL people.