Difficult but possible. The shinkansen from Shin-Osaka to Tokyo goes through Kyoto. The problem is luggage. The few larger bag lockers at Kyoto Station are often full and most are size-limited. If you could forward luggage from your Osaka hotel to the hotel in Tokyo via "takkyubin" delivery and just keep a small backpack or hand bag of what you need for a couple of days, it would work better. Leave the small bag in a coin locker at Kyoto Station and have most of a day to see a little of the city before continuing to Tokyo in the late afternoon or evening.

If doing the above, I'd plan to bite the bullet on expense and use taxis to move from site to site, saving time and hassle. With a group of 9, you will need at least 2 large cabs or 3 smaller ones unless you can find the occasional van-cab. Perhaps a better suggestion would be a guided one-day visit with Doi Taxi. Doi-san has a van that should accommodate the whole group. If you do that, be sure to reserve ahead as his company is very small and quite popular. http://www3.ocn.ne.jp/~doitaxi/about_kyoto/index.html