If you haven't already done so, be sure you make your ADRs (advance dining reservations). That's the beginning of the busy summer season and you won't just be able to walk up and get a table for 10.
Make sure you get to the parks at opening and make good use of the fastpass system. Just send one person to collect everyone's fastpasses - that takes less time. And remember, Fastpasses are good until park closing on the day you get them. A lot of people don't know you can use them past the printed window on the pass - never before the return time, but always after the return time until park closing that day. Take a look at
www.touringplans.com to get a look at which parks are best for which dates. Gay Days will be going on June 4, 5, 6 and 7 so, in regard to crowds, you may want to avoid those parks that are having those designated events on a certain day. Unless your family is going to participate in Gay Days, then you probably wouldn't want to avoid those park days.
As far as splitting up, we don't usually split up. We like to have the WDW experience with our whole group. But, I'm sure that differs from family to family. Also, we haven't had any issues eating with a big party. Just make sure you get to your ADR about 15 minutes early to check in.
Hope ya'll have a magical vacation!