You're doing all the right things. I see that you've tried activity toys. Does that include a Kong or other type of food toy/puzzle? If your puppy is food-motivated, a Kong with some kibble and peanut butter, treats, and/or frozen with chicken broth and treats may work. I recommend giving her a kong with something delicious in the crate while you're home first. And only give her the kong when she's in her crate. Then when you take your other dog out, give her a Kong in her crate.
I also recommend tiring her out first. A fun, tiring play session in the backyard followed by a filled Kong in the crate might be just the answer.
Side note: Are you not walking her with your older dog because of her age/vaccinations? If that's the case and you haven't already, I recommend getting her into a puppy kindergarten training class so she doesn't miss out on socialization with other dogs, people, environments, etc.
Is she the pup in your avatar? She's adorable by the way!
#PetBehaviorandTraining