The unusual purpose that tobacco serves in this book is that of a tranquilizer. The family uses tobacco smoke to calm and tranquilize at least three animals or groups of animals in the book.
First, Fritz wants to make a pet of the eagle that they have caught. However, the bird is too wild and Fritz is ready to kill it. However, Ernest tells him to blow tobacco smoke up around the bird's head. Fritz does so and that makes the eagle calm down. Later in the book, they will do the same thing to an ostrich.
In between those two episodes, the father uses the same technique on a swarm of bees. The family wants to get the bees out of a tree trunk and into a hive. In order to calm the bees down and make it possible to move them, the father blows smoke into the tree trunk. This calms the bees.
I do not know if this would work on eagles or ostriches, but I have worked with bees and I can say that people do use smoke to calm bees down. Follow the link below to see a picture of a beekeeper with his smoker.