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I don't think so. Maybe the willow tree has a power to the soul can stay there (in my country, I heard the elderly tell me some trees have this power). If the father killed the mommy and burried her under willow tree, he would never let his son see that tree. He wanted to hide it, right?.The soul of the mommy did not want to disappear because she always worry about his son, so she was there. The farther remarried after his son had a family. When he became weak and old he need a person beside to help him.so I think he loves his old wife,too.
Did the mommy died and became the willow tree? I read a similar folklore before where the father murdered the mommy to marry a new mistress and buried the mommy under a tree. The mommy spirit always watches over her son.