Free implant + cash settlement.
Implant doesn't quite make it right, because it's still inferior to the natural tooth, and there's always the possibility of complications. Plus there's the hassle and pain associated with the implant itself.
I would start off with something like, "We just want something fair. This is a pretty big deal what happened, and something needs to be done to make it right."
Claim is probably against the extracting dentist.
That dentist does not know that the family member is litigation-shy, so you can bluff as far as that is concerned.
The best general approach is to not directly threaten anything, but to be firm and make it clear that your family member needs to be made whole Dropping statements such as, "We just want something fair" is important, so it gives them the impression that you're not trying to get rich off of this, but at the same time, won't accept lowballing.
The extracting dentist may want to avoid an insurance claim, especially if the amount you're asking for isn't high.
Here's a site discussing dental malpractice:
https://www.hg.org/legal-articles/ha...practice-23428