I think one of the first suggestions works best - go together to places you all are reasonably happy with, and go your own way for those you aren't. Have everyone do their research and come up with some ideas of where to go - browse this website, as well as the JNTO page (www.jnto.go.jp) as well as the official city websites with their own tourist guides.
Japan offers something for everyone - there are many places you could go together, if you all are flexible enough. Two weeks only in Tokyo would be such a waste. There are many good day trips you can take, and even in the "Concrete Jungle" of Tokyo, there are a dozen beautiful historical gardens you can visit.
https://goo.gl/tAECfMFor times you are not together, I highly suggest you find ways to communicate (get SIM cards or pocket wifi while in Japan) to keep in touch. Or find a 7-11 or Starbucks etc to use their wi-fi if you need to contact each other (you may need to register ahead of time). There is also some free wi-fi provided by some cities but many are dissatisfied with the connections.
http://wi2.co.jp/tjw/english.htmlhttps://www.sej.co.jp/in/en.htmlhttp://kanko.city.kyoto.lg.jp/wifi/en/If one of you doesn't want to climb Fushimi Inari, then either you all can go partway up, or she can go partway up and wait, or she can go somewhere else (Tofukuji is nearby, and is extremely nice). Nobody can impose anything on all of you - you need to compromise or find an independent route everyone is happy with.
For food, as well as the religious aspects, it's up to each person to decide what to do. The more rigid you are, the more difficult things are going to get. You could browse Tabelog or Bento for example for some databases on places to eat.
https://tabelog.com/en/https://www.bento.comOr go to a vegetarian place, or get your food at a convenience store, supermarket, etc. I wouldn't go running all over the city for a specific place unless it was something special.
I can understand your brother's viewpoint given his age. Kyoto may be less his thing, but there are still many places that he might like (the Railway Museum, the Sagano Railway & Hozugawa River Cruise, Toei Studios, Murin-an Garden, Iwatayama Monkey Park, Nishiki Market, etc). For anyone really, if you just go see temples and shrines, and temples and shrines, and then more temples and shrines, you are going to get "templed out" and your eyes will just glaze over. Adding enough variety is the key.
https://goo.gl/knQtMgThe same can be said for Nara (which you should not miss either).
https://goo.gl/LfvWnLAside from the Todaiji Temple which is killer, there are other things like feeding the deer, seeing the Isuien & Yoshikien Gardens, etc.
For a successful trip, all of you need to do your research and cooperate for a satisfactory itinerary.