I don't blame your daughter. She's not even two! She had no idea a tree (or part of a tree) could be hit like that! Good gracious! What has happened to her world!? She's wondering what might happen next. Don't let anybody say that toddlers don't have imaginations.
This is going to be inconvenient, to say the least, but I think I would go ahead and sit with her. (Hopefully, Daddy and even Grandma or Grandpa could spell you sometimes if they're around.) I would tell her that even though storms can hurt trees, most of them don't - but that I'll be right there to take care of her no matter what happens. Get yourself a cup of tea, and her a cup of milk, and sit. Don't try to distract her, but maybe you could sing, or softly tell her stories.
It will take some time, but your calmness in the midst of the storm will eventually teach her to be calm. Eventually.
You don't have to tell your little girl this, but just for perspective for you: one of the classic stories at my house was the time my mother's family went through a cyclone. She hadn't been born yet, but three of her older brothers were there, along with my grandparents. The cyclone blew them right out of the house. They weren't hurt, but the house was totaled. (This was in East Texas in the 1890s.) My mama said that after that, until the 1940s when she died, whenever my grandmother heard thunder she headed for the cellar.