My father is straining our relationship

For starters I'd like to note I had a pretty decent child good and am very close with my parents even tho I live on the other side of the country.

Now for the situation.

My father constantly slanders me to my sister in law and her friends.

Last year I was in a really bad car accident that almost took my life on the way back to their house with my 2 daughters and my dog. My girls and I ended up flying back home due to lack of a vehicle but had to leave our dog as he is to big to fly. We had been looking into shipping my dog when my dad offered to buy me a puppy for my birthday. I refused, and this went on for another month. Well turns out my dog and my father have become very close and my parents dog is on his way out so as a gift my husband and i decided to let my dad keep my obedience/ protection trained german shepherd. My father seemed very excited.

Today I called them while they were out and my sister in laws drunk friend was yelling to the phone that I need to take care of my dog.....

This wasnt a situation where I have just dropped my dog, my father repeatedly asked to keep him and now i feel like he is making it sound as though it's a burden to him.

This is not the first time hes done something like this and it makes me feel bad to know my father is sitting there talking bad about me to these girls..

What would you do?