Michigan: My Cousin's Mom Is Giving Away Her Dog Without Her Permission - Help!!

Location: Michigan

I should preface this by saying that I am not an American. I am European, living in Europe. However, my cousin is an American, who is currently visiting Europe for about a month as she's taking a break after receiving her master's. She's 25 years old.

She has about a 6-year-old golden retriever, who is currently temporarily staying with her parents as she's away. She was, as far as I understand, under the impression that her dad was going to be the main person looking after the dog, as her mom is genuinely not mentally well. Also, her mom's relationship with her dad has been deteriorating for about a year now. Her mom hasn't seen a doctor about her issues, doesn't believe in it, and believes in all types of conspiracies on top of that.

Well, her dad had an emergency of his own a couple of days ago, so the dog was left alone with her mom. The mom is convinced that dogs are not going to be legally allowed in Michigan anymore since a couple of days ago, and has been trying to make arrangements to give the dog for adoption to a different state.

My cousin has called her dad and practically yelled at him to go back and get the dog, and maybe put the dog in a daycare facility until she gets back, but he's not going to be capable of going back to her mom in the next few days.

Her mom doesn't really speak to her, aside from going on absolutely psychotic rants over the phone.

The dog is microchipped, I believe under my cousin's name. She has been calling a lot of her friends, but most of them are working or going to school in a different state and cannot just make the drive over to pick up the dog.

What can be legally done here? Can her mom just give her dog away without her consent?