Indy 500 ~ I think I depends on how your family wants to ride. I have felt the Eagle River area is nice been there more the once and have always liked it. It gives you lots of direction to ride in, and let you adjust your ride length with different trail loops. Which depending on your mother and sister you may want. You have a lot of choice a far as lodging goes, I have stayed at the Days Inn and Best Westerner, and both have pools. One place I have wanted to stay is the
Hiawatha Motor Inn I believe they are a supporter of JD site also and he does great trail reports with picture from his rides. Plus there is lots of other place to stay, however that does mean more people in one area. And the trail will show that on a Saturday night no matter how much grooming they do.
Depending on the location in the UP you can find that same style of riding or more of the railroad grade riding with much longer loops, but really nice trails! I would recommend Rockland or North. I have only been there once but enjoyed every minute of it. When I went I took my wife and a friend and his dad. My friend and I were the seasoned riders. His dad use to ride every now and then, but had not road in 20+ years. And you’re too young to know how a wife can complain, when she is not happy, but we had no complaints out of anyone in our group. We all enjoyed ourselves!
Western UP Feb 4-8
Also you mention you were not sure if you could convince your dad to register your sleds in Michigan. You do not need to register the sleds in Michigan Just get a trail permit. I think it is $35 each this year. Also if you rent sled from somewhere that is by the state line most place will have paper work to be able to ride both states. I think Trackside did this with their rentals as well. At least you would not blow money putting trail sticker on rental sleds. But check if you plan on renting and then riding in the other state.
Good Luck with where ever you pick!