Assuming she has experience in school, send her into the ladies' and wait outside for her. In the case where YOU or her brother have to go, use a companion restroom and have the two of them wait together outside the door. (In a year or so I'd say she can wait outside of the regular men's room, but there is more traffic there and the number of men can be a bit intimidating, so at first I'd try having her wait at the smaller ones.) If you can get to the child-care centers, great, but most of the time you won't be on that side of the park when the moment hits.
One thing that is very important: if either of the children are waiting for you, PUT them in the spot before going inside. Some of the WDW main restrooms have two exits, and you'll want to know exactly where the child is supposed to be waiting. If they are supposed to come back to you and you appear not to be there, tell them to go directly BACK into the restroom and look for another exit; they should assume that they are at the wrong door, not that you have moved. (Honestly, we still have this problem with my directionally-impaired DH; he'll tell DS to meet him outside the men's room, and if he doesn't see DS when he comes out, never thinks about the possibility that HE is at the wrong door. Note that DS is a grown man now; he doesn't want to look like a perv lurking around INSIDE the men's room either.)
Now then, others can flame me all they like, but this current US trend of taking children into crowded opposite-gender restrooms until they reach puberty is bizarrely paranoid. If a child is in a regular school every day, he or she knows the rules about public restrooms. As long as they are in good repair and have plenty of traffic in and out, they are no less safe than a city sidewalk, and probably more so. If the place is isolated and apparently deserted, yes, by all means, go in and inspect for lurkers before sending children in, but at Walt Disney World there are FAR too many potential witnesses moving in and out of those rooms for them to be dangerous in terms of foul play.
As for the grown woman shoving a kid out of the way, she'd probably do that anywhere that she might be able to get away with it, including a ride line. You can't live your life constantly on guard against oddities like that.