One night in Hiroshima – help planning peace museum visit and Miyajima

I am staying one night in Hotel Granvia in Hiroshima and we'd like to visit the peace Museum and go to Itsukushima Shrine / Miyajima. We cannot stay up late due to travelling with a baby so by 6-7pm, we gotta be close to bed time. We are coming in from Kyoto and going our to Osaka.

So I am wondering if we should come in early from Kyoto and hit the museum or go to Itsukushima Shrine / Miyajima first then do the other first thing in the morning before checking out and heading off to Osaka. I also heard there's a cool cable car thingy up the mountain but I doubt we'll have time for that.

Any tips?