First off, Hi! and welcome to Pet Talk! Your pets are adorable.

I went through something similar when my roommate moved in. They have a cat(Snowball) that had a bad past experience with a dog and was understandably afraid of them. Thankfully my dogs grew up around cats so they don't bother them at all, so within a week Snowball felt comfortable enough to be out and about among the dogs.

Its pretty natural for cats to be afraid of dogs, especially one that hasn't grown up around them. They are just looking out for their own safety until they know that this "strange creature" isn't going to cause them harm. Have Ava and Mizzie met face to face... how'd that go? And does Ava go out of her way to bother Mizzie?
As long as Ava isn't the type that chases or pesters cats, then I think your transition should go just fine. Make sure to give Mizzie plenty of places to get up and out of Ava's reach (such as cat towers, shelves, etc.) so she feels more safe. Its okay if she hides for a bit, just give her time and eventually try coaxing her out with some yummy treats. You can at least give it a shot for a few weeks, and if Ava truly seems miserable it may be best to take her back to your grandparents.

Best of luck!