but why did she come back ?

She didn't forgive them. After all, she had still been separated from her son in life and he had still died a premature death. It seems that she will continue her grudge forever.

Because it's a horror movie

In my opinion she wanted to thank him by reuniting him with his wife and solving his financial problems

After they buried her and her long lost son together in a grave I thought her soul would be at peace. So why did she show up at the end for the boy?

Sorry, but this was one vengeful woman. She didn't kill Arthur and his child to thank him, she was simply continuing her vengence.

Between the supposed appeasement of the Woman and the taking of the child (and his father) on the train tracks, there is a transitional moment where a short sound clip of the Woman saying "I'll never forgive you" (or something similar) played atop a flashback of the letter she wrote which included that line. You may have missed it because all the reverb made it hard to understand, and her handwriting was fairly indecipherable as well. In any case, this transition was meant to tell us "No, she is not appeased. She will never be appeased. She will never forgive," and to thus prepare us for the attack on the Kipps child. At that point, we knew she would be coming for the boy, we just didn't know if Mr. Kipps would be successful in intervening. In the end, he was, and was not. It was a bittersweet ending, featuring the irony that, in trying to devastate Mr. Kipps, the Woman inadvertently reunited him with his wife.