I think that the key to this will be direct, upfront communication about everything. And of course, if you and DH are vacationing with six other people, four of them children, it almost certainly will
be a different vacation style than you're used to. Flexibility will also be important. You won't
get to do everything you want to do with everyone present, because the others can't afford it, or the kids are tired, or they simply want to do something else that you aren't interested in. So you'll have to decide what you're going to do--always keep the group together, even if that means doing things you and DH don't want to do, or splitting the group up sometimes so people do what they want but separately.
I definitely don't want to put you down, because you seem like a very generous person; but I feel like you might have an image in your mind of how the whole vacation is going to go, and how everyone is going to act and feel, and that might not end up corresponding with reality. For example, you started with the assumption that Casey would be thrilled that someone wanted to take her kids to WDW without her, and that she would be touched and pleased that you went around her to her parents and other relatives to figure out how to pay for her kids to have this experience, so she wouldn't have to, because she can't afford it. And honestly, I don't know, maybe that's exactly how it would be.
But it seems like you're now starting to realize that maybe Casey could reasonably have a different feeling about it--maybe she would feel patronized or like she wasn't in control of what was happening to her kids or like people think she's not a good enough parent. Maybe she wants to experience WDW with them the first time, or she doesn't think they'd like it/she doesn't like it, or she's been saving up for some other gift to give them that's big in their world but would seem paltry in comparison to a trip to WDW. Maybe she can well afford more than people seem to think, but she has different priorities.
I think when you want to and are able to give a huge gift like this, it can be very exciting and it feels really good, but there's a risk of overwhelming the people you're gifting, especially if you present it to them as a complete package that they have no input in, with all kinds of emotional expectations inadvertently attached. They may not react in the way you're hoping they will, and that could just lead to hard feelings all around. I think it's important to be aware of that--you don't want expectations and logistics to ruin the generosity of your gift, which is to experience one of your favorite places with some of your favorite people.