I'm not sure if this the reason, but as an ex-cast member, I think I might know why DFTW is saying no kids at the early morning Epcot photo shoot. I'm assuming that the photo shoot takes place before the parks regular opening hours? (If thats not the case, just disregard this)
Typically Disney will not allow kids (usually anyone under the age of 16) on the "backstage tours" because it will spoil the magic for the little one's if they see certain things (Mickey mouse body...human head...deeply traumatizing for a small child). Even if your kids are pre-teen or so, Disney will not bend the rules to allow kids (even those that know that Mickey isn't "real") access to backstage areas. Before the park opens there's often alot of...less than magical things happening, that Disney probably wants the least amount of people (especially children) exposed to.
I really hope you don't change your wedding plans because of this. Like the other posters have said, have a seperate photo shoot (in "regular" clothes) with your children another time. I understand how much you want to include you children (and that's a wonderful thing), but having some photos of just the 2 of you, will also give you some wonderful memories. I'm sure you will have plenty of photos in your wedding attire with your kids (dressed up, of course) from the actual wedding.