You said you have arranged for in home pet sitting. Then you talk about boarding and taking cat with you. Why aren't you going with your first plan?
You mention your daughter is against boarding. Is she also against in home pet care? How old is she? If she's a kid, why are you letting her make this decision?
I've had several cats and left them at home with a bag of food and a barely trickling water spigot and large bowl of water, when I traveled. They were fine. Cats are loners. My current cats hide out in the basement. So.....the argument that cat will miss you is not a reason to take him with you. It's likely the cat will miss you but he will be Ok. He will not be traumatized.
When I moved and was on the road 3 days, I took our cat in a rented small truck. He had access to both front and back. I took a litter box. I left him in the truck when I stopped for the night. He was happy.
I believe that pets, while part of the family, the people make decisions that are best for the family. I've taken a well behaved dog with me on short trips. He was anxious, needing much of my attention.
Will having the pets with you enhance your time away.or be more of a burden. Will they enjoy the time?
I would not board an animal. They will be confined in a cage most of the time. They are also exposed to germs and possibly be sick.
In my experience, the cat was better off staying home.
As to the mice, I always asked someone else to pick up bodies. Then a few years ago, I was the only one to do it. I put my hand in a small bag and picked it up like picking up dog poop and dropped it in the garbage can. Provide plastic bags. Hire someone who is willing to try it.