i am interested to know how you know what a dog thinks and feels! - its more likelythat its how YOU feel (ie excited when she arrives and sad when she goes)
Ok, so she seems sad when she leaves you but dogs are very adaptable, and for all you know she is also sad when she leaves your auntie!
I don't really see hw you could prevent falling out with auntie, if you start using legal language towards her despite the fact she has already said she dosent want the dog to live with you ful time.
The dog belongs to your auntie, and she has a right to ask for it back whenever she wants. If you think all the back and forward is upsetting the dog, or if you get sad when she leaves just dont have her next time