I thought that during this time frame, women could not inherit property in England, which is why Scatcherd left his estate to his son and not his wife. But yet his niece was able to inherit. Why not the wife?
I think you might be confusing inheritance with an entailment. Estates were often entailed along the male line. This is seen in Pride and Prejudice, where the Bennet family estate is entailed to Mr. Collins, since Mr. Bennet never had a son. However, estates were not always entailed away. Again, from Pride and Prejudice, Lady Catherine de Bourgh only has a daughter and remarks on how the de Bourgh estate is not entailed away from her daughter, who will presumably inherit it upon the death of Lady Catherine herself.
With that said, I'm not familiar enough with 19th century wills to say why Scatcherd selected his son and then niece to inherit. My only guess is that he wanted to pass the inheritance on to the next generation, not to someone who was already advanced in years.
The inheritance of Downton Abbey was much discussed on that show. There was an entailment and the house and lands went to a distant cousin who was a middle class lawyer. He moved there and after a lot of pleading by her parents the daughter Mary married him. He could have kicked them to the curb if he had wanted.
Exactly and that's also why it was such a big deal to have one of their daughters marry the heir because it would secure their safety. No way Matthew would kick out the mother/siblings of his wife. Also why Mrs. Bennet was so insistent on Elizabeth marrying Mr. Collins and Mr. Collins' intentions to try and right the wrong the bennet's felt.
Women could, indeed, inherit property. Scatcherd wanted to leave his property to his heirs in the next generation. It was his way of making certain it passed to his own bloodline. If he had left it to his wife, she could have disposed of the property some other way, including donating it to the church if she had so wanted.
Scatcherd made generous provision for his widow in his will. She would have lived in comfort and luxury for the remainder of her life.