I have used paper towels, but prefer blank (un-printed) newsprint paper for wrapping fresh soap for transit. It is fairly easy to find at stores, but I save it when it is used as packing material. When I don't have newsprint available, I often use freezer paper to lay down between layers of soap in a box, just to prevent them from touching each other. I have even used printer paper as a temporary wrap for soap while traveling. But my go-to wrap is blank newsprint. It just seems to be the better of anything I have tried. I even tried tissue paper, but it can be problematic if the soap seeps even the slightest little bit, which sometimes happens with fresh soap and/or temperature changes. Then I pack them into cardboard boxes and put into the trunk of my car. This time of year, I wouldn't expect a lot of temperature fluctuation from Minnesota to Washington state that you'd have to worry about, so your soap should be fine if it just stays inside your car the whole time. I've left soap in my trunk for 3 or 4 days on roadtrips and not run into any difficulties. Once my soap was in the trunk for 10 days in the trunk wrapped as I described (in a covered parking garage) in the Pacific Northwest and suffered no ill effects. But I did add some desiccant packets to the cardboard box that contained the soap that time.
I hope all goes well for your family.
