Warning - My personal bias is showing here; definitely, not everyone feels the way I do. Also a bit hard to suggest as your personal interests and ages of kids are unknown. I'm just sharing some thoughts - they are mine, not everyone will agree. That is totally fine - we all react to our travel destinations differently!
Osaka is a vibrant, busy city that is excellent for work assignments, but, in my opinion, Kyoto offers much more for tourists. Since the two cities are only a 15 - to 45 - minute train ride apart, you can easily stay the extra nights in Kyoto and visit Osaka as a day trip if tempted by its offerings. I do agree, staying in Osaka makes sense if you have an early morning flight.
I can't imagine that your tour will touch all that Kyoto has to offer - for instance, will you be visiting the Arashiyama area? Way too much to see in one day. I've seen most of the recommendations here. All worthwhile. https://www.japan-guide.com/e/e3912.html and https://www.japan-guide.com/e/e2158.html
Nara and Himeji recommendations are great. Himeji Castle and gardens, if castles are not included in your tour, would give you something special to enjoy. Fushimi Inari Shrine is another option. (My guess is your tour might include this.) All of these day trips can be done from Kyoto as well as Osaka.
Osaka - https://www.japan-guide.com/e/e2157.html I've been to many of these spots. The link to Minami (Namba) includes a description of the street food available in Dotonbori. As you note, that is a fun area - lots of neon signs of great creativity advertising restaurants and food stalls. Day time works as well as evening. Osaka Castle is rebuilt and contains a museum - it is not a trade-off for the more original Himeji. If you are very interested Japanese history, that museum and the Museum of History are rewarding. If not wanting to read signboards and spend time with exhibits, other options might be better suited. The Aquarium gets rave reviews, but I found it disappointing - fun architecture, you start at the top and spiral downwards through exhibits somewhat like Boston's Aquarium, but it just didn't hold my interest the way other aquariums in the US and Asia have. That could well be my lack of imagination - there are Youtube videos you could review if you were interested.
Hiroshima is doable as a full day trip if your tour doesn't include it.
Bottom line - you will have no trouble enjoying yourselves! The website guides above are the best I have found in a number of years of visiting Japan. Other options for research that I've used are "Inside Kyoto" and the official city guide. https://www.insidekyoto.com and https://kyoto.travel/en/