"The belt is just an object around the waist. Ideally, the belt should do what belts do and restrain the dress. But not in this case. The dress sim will immediately envelope the belt like it's not even there. 3D Mobster has the same idea I did, which was to restrain the dress around the waist, but I really want to know why the dress isn't restrained by the belt even though it's set to collide."

Here is an example of how you can do it. I created a belt and an old dress i had, so nothing fancy, but it will suit the purpose well. They are two seperate objects, which the colors show.  

So have imported both objects. And i have scaled the belt so its around the dress and victoria as well.

So in frame 1 i have scaled the dress to 119% and in frame 10 i tighten it down to 104%. The belt is really tight at 100% and will match victoria, so i leave it at 104% so there are some room for the dress, you can ofc experience with it, and also this is done really fast, so to avoid to many problems ill leave it like that.

 

In the cloth room i have these settings for the dress colliding. The belt is not part of the simulation yet, except as a object for the dress to collide against.

As the simulation is calculating, the belt is tighting around the dress. Since frame 14 is working fine, ill export the dress (Only the dress) in frame 14, and delete it from the scene, then import it again, so it now looks like frame 14 in frame 1. Then ill move the keyframe of the belt scale to frame 1 as well. 

Now the dress and belt looks like it did in frame 14. Next ill export the dress and the belt together. Using the above settings. Delete the old ones from the scene, and import the new combined dress. 

In the cloth room i setup contrains the belt and then i have selected the parts of the dress under the belt and just around it. So there wont be any poke throughs. You should probably spend a bit of time doing this correctly as i just rough it pretty fast. so there will most likely be poke through with certain poses. 

When that is done, you can calculate the dress as a single object like a normal dynamic object.