Who cares? Everything you say is true--she was, financially speaking, stupid to turn down his offer, and ended up selling the house for much less than he offered. But none of that gave Trump any right to use his government cronies to take her property and give it to him. (Also, it's worth noting that when Trump and the CRDA tried to use eminent domain to take the house, the compensation would have been much less than Trump's original offer - somewhere around 250K).
It may not have been about the money. My guess is that she held on to the home in hopes that her kids would eventually move back to NJ, and they would have a place to stay while house-hunting. The amounts requested were perhaps an excuse to fob off her kids' request that she move to CA. I've encountered situations like this, including one where a Holocaust survivor finally moved out of his apartment in his 90's, after he felt he could no longer manage. Having to trade familiar surroundings to be with your kids is very, very hard. They can start over. The elderly have a much harder road.
Thank you for making the essential point here.
Obama is in the process of using it for his library.
The Clinton's used it for their library.