Yogi and Gracie Ruth are this exact same way!! We have 2 of the same of many toys, but they only want the actual toy that the other has. Yogi is the worse as he is bigger/stronger and can take the toy easily from G. We've been working with them both to not steal the toy, but to wait until the one is done playing with it. Yogi will lay down just a fraction of an inch from G and stare at her until she's done.
However, at times G likes to taunt Yogi with it. She'll stop chewing on it but it's right at the tips of her paws. She'll look at him and do this funny little woof-huff, as though daring him to try and steal it. Of course he can't resist and tries, she'll snatch it up and bolt off, yammering back at him, "Nanner-Nanner-Nanner, I've got the toy" He'll run off after her and then the chase is on. During that time, if he get the toy away from her I don't scold him...the game has changed from chewing to the chase. They are so comical, I could watch them play for hours.
