Osaka sits 15 minutes from Kyoto. Use that. Do not treat the city as a station sandwich on the way to Hiroshima.
1 night: Dotonbori from Kyoto
Afternoon castle or Kuromon, evening Dotonbori, morning train to Hiroshima or back to Tokyo. Tight. Fine if 10 days are already full.
2 nights: kitchen city
Day one: castle and Dotonbori. Day two: Kuromon and Umeda or Shinsekai. This is the Osaka chapter on the classic 10-day route.
With Hiroshima
Shinkansen about 90 minutes (Hikari/Sakura on a JR Pass). Day-trip Miyajima from Hiroshima, not from Namba at 6am.