What if the "prey drive" kicks in the GS when you are not home?
I have a GS/Great Dane Mix outside, 13 yrs old, who loves my youngest 5 lb Yorkie. I NEVER leave them alone together. IMO no matter how well trained a dog is, instinct takes priority over training. After all, these are dogs, not human children no matter how much we wish they were human. Just my 2 cents. If you have to, I would crate my yorkie when you can't be home.................................