When we went with a large group several years ago, we pretty much split up most of the time. We went in different combinations of people each day, so everyone had the chance to be with everyone else. We had 24 people there, so only did one real dinner with everyone together. I arranged this with Whispering Canyon Cafe at Wilderness Lodge. We had the little private area toward the back of the restaurant just for our group, which was perfect.
I did my planning as usual and filled in everyone else as to our dining plans. Several of the other groups made reservations at the same restaurant as us at about the same time, but we generally weren't seated together, which was OK. As to which park we went to, my parents, grandmother, grandmother's friend, and one brother and his family plus my family pretty much all went to the same park each day...the one I picked. But, we didn't stay together in the park all day. We arranged a meeting time later in the day if we split up. The rest of our group did what they wanted to do (this included another brother and family, my cousin and her son, another cousin and his family, 2 sets of aunts and uncles.)
You've got it wonderful by staying on Disney property. When we went, my mother arranged the location to stay, which was off site. At least with staying on property, if someone wants to head back to the room for a while, they can. When staying off site, we pretty much had to stay together for transportation purposes.
Having my parents with us did work out well one evening. They watched our daughter so we could go to dinner by ourselves. We enjoyed a wonderful meal at Victoria & Albert's.
I hope all works out for you. Perhaps allowing everyone some flexibility will work out as well for you as it did for us.