It is pretty simple, in fact. It only becomes complicated when you remove all the constraints that were applied implicitly during the creation of the original, and every part of it becomes separate. Which is the program's behavior that I'm complaining about.

Here's an image of my sketch, showing one possible result of applying some but not all required constraints to the second instance before altering the key dimension.
The required geometry is a circle with indents. The indents are simple triangles of a given height (1mm). The defining dimension needs to be the diameter of the inner circle which goes through the points of those indents. So, I created a construction circle with two construction radii for reference (only really needed one). I then created another concentric circle outside that and defined the distance between the two. The indents were created by drawing one line, mirroring it, then selecting those two lines and creating a circular pattern. I then broke the outer circle to make the resulting profile simple, while retaining the work geometry so that no references would be lost, so the copies could be altered correctly. Or so I thought.
I then created a rectangular pattern of these objects. After searching again to see if they had yet implemented a checkbox to de-link them during the process of creation (sigh), I figured out how to delink them again afterwards in order to be able to resize each of the others (and why can't I delink just one instance? Nevermind). I then dimensioned the second instance by dimensioning the inner construction circle. But it didn't work. It simply changed that circle's diameter and left all the actual geometry I cared about untouched. I tried many solutions to fix this. If I defined the dimension on the distance between inner and outer circles first, it only applied to one outer arc at a time. If I explicitly dimensioned the difference between the inner circle and each outer arc (as shown in the screenshot) it still ignored the coincident constraints on the points of the indents.
If I go back and attempt to explicitly select every single constraint, first of all, they are hard to find, and always unnecessarily hard to identify, and second, it doesn't seem even to have a constraint selectable for the points of the indents. But in any case, even with them selected, they won't copy to the rest of the pattern. This should absolutely work when explicitly requested by the user. (Same for dimensions.)