A.B.
I highly recommend telling her the truth. She can handle it. Exposing children to safe pain will help them learn coping skills even at that young age.
She will get over the situation and you need to make the family the priority. I recommend explaining to her that you want to focus more energy on playtime and fun family time and the puppy takes away too much of that. The puppy is also not getting the attention that he needs from you because you don't have enough time to take care of him. This other family will invest the time and take care of him and he'll be happier. She'll get it as long as you're comfortable and confident with what you're doing.