Hi!
This is the best site for calculating tolls in Japan:
https://www2.kumagaku.ac.jp/teacher/~masden/tolls/It does matter when you travel. In my case, I was traveling in the middle of the day to a rural location and then was heading towards the main city around 17:00 which is the opposite of what someone commuting would do. I used a TEP Pass for my second rental. I rented from Ichinoseki, so while their English and my Japanese made renting take longer, I never had any real traffic or difficulties on the road. I used the free GPS on my rental. I have no idea if yours will have that as well. I was driving only in Tohoku so I didn't have any traffic and the roads were mostly empty. You are not, so your experience I expect will differ dramaticlly.
Here is the US a FIT is considered a very small car, but I know standards are different in Japan and in Europe.
You need to look at your kid and realize what they like. I enjoyed Matsumoto Castle, my child did not. They did enjoy the art museum though and getting drinks from the free fountains around town. We're going to try the monkey park probably next trip, in the past, we went to see the monkeys in Kyoto. That was very popular. As of 2017, Nara still had deer crackers for sale but Miyajima did not My child still really enjoyed Miyajima though we didn't climb Mt. Misen. She much more enjoyed walking out to the torii and watching all the crabs on the sand. I have been up Mt. Misen. It's OK? My kid loved Hida no Sato village. They had a lot of organized activities. We were there in the Summer, I've no idea what March will be like.
My child usually has no issues adjusting to Pacific time from Eastern time (about 3 hours) and after a few days adjusted to Hawaii which is 5 hours off, but has a hard time with Japan because it's a good 13-14 hours ahead of Eastern time, I'm a bit nervous about the 16-17 for Pacific. We have taken my child to Europe (in August) and the 5 hours ahead made for lots of late nights. It worked well because it fit our relative's schedules better.
I think by car you are seriously underestimating how much time you are going to have in certain locations, particularly your Hiroshima days. If you leave Osaka, it is going to take you a minimum of 1.5 hours to get to Himeji. You then need to find parking. You then visit the castle which might be quite crowded since we're talking close to sakura season. You then have another 3-4 hours drive with no traffic to Hiroshima. You then have 1 day the next day to try to see Miyajima and Hiroshima? And then the day after you are trying to see Okunoshima and then drive 4.5 hours at a minimum to Kyoto?
I know my kid hates long days of travel. Multiple days close together of 5+ hours sitting in a car (or train) is not something that mine likes. Maybe yours does, I don't know... but I now try to keep trains or driving to no more than 3 hours if I can help it and if we do longer, the next day is shorter. Be prepared to pay more for ferries. It would be 450 yen for all 3 of you to take the ferry to Miyajima. With our car, it will be 1060, and again, even if you are just driving your car to park it be very very careful. The deer are not terribly wild and will wander everywhere. I have seen them in the ferry terminal. They are not going to run out of the way of your car. People will not be looking at cars. The speed limit will be low, but hitting a person or deer is just going to not be fun. The same is probably true for Okunoshima and the tourists and bunnies there.
You will also need to find a lot for visiting Magome and Tsumago since I believe the whole point of the area is to make you feel like you've slipped back in time.
I would not spend 2 days in Osaka. Outside of shopping it's pretty similar to Tokyo. I mostly go to see my friend who lives there.
Spend some time making sure you can find someplace with parking in Kyoto, Osaka and Hiroshima. None of those places are really car friendly. I very very rarely see hotels offer parking, even paid parking, the sorts of hotels that offer paid parking are not likely to be super budgetary, since the most budgetary places don't have the space to offer parking. If you pick somewhere further from town, you will need to commute in which will take time.