This is exactly what I was going to suggest. Traditionally, someone is with the child while other guests in the party go onto the ride, then have that person go onto the ride after the other guests return. However, if that is not possible, as others stated, there are not only strangers, but TMs that are there (which I'd hope would reassure her more), films that are shown, and it is purely for only the duration of the ride. Which SpiderMan for example is five minutes. I want to also state that rides either have the rider swap right at the end of the attraction, or have an easy access point to the rider swap area. You can always ask a TM.
However, another option and I do not know how comfortable you are with this, but I am assuming your son could be the 12 year old and if your son is tall enough he can go on the attraction himself while you wait with your daughter, from there he can wait with her while you go. I suggest this as I started relatively young doing SR lines with my father and worked well as I've always been good at listening to my parents and we established a spot at the end of the ride we would wait in the end for the other.
Also, I do want to say even though this is a little off topic that if it is just you and your two children (which I do not know if it is) to establish a meeting place in both US, or IoA in the case that anyone is separated. As it can happen just in general. We started that when we first went to the parks and although it's rare I have my parents with me, still do it when we all do happen to go. Might be grown now and have cell phones, but it's just a good thing to establish possibly. As running around trying to find someone isn't helpful if the other person keeps running around looking too.