Ok, I can make it work using snapping only (no guides), in only one way, which instead of snapping the center of object 1 (of the group) to the center of the rectangle, is to snap the center of the rectangle to the center of object 1 (of the group). Here's how I found that will work.
First, set up the snap control bar like in my screenshot (which essentially is disable every option except for snap to centers). (Actually, snapping to grids and guides could still be enabled, if you aren't using any grids or guides in your file.)
I find it helpful to click twice on the objects, to see the rotation centers, just before I start, to make sure I'll be dragging the centers close enough to each other - especially if object 1 has an odd shape.
Then, the center of the rectangle should readily snap to the center of object 1, as long as you are bringing the center of the rectangle close enough to it.
In case you can't move the rectangle, here's a way to snap the center of object 1 to the center of the rectangle, and still keep object 1 and object 2 relative to each other. They can't stay grouped, but they will still remain in their original places. The same configuration of the snap control bar will work for this.
First, ungroup the group with object 1 and 2, but don't deselect anything. This keeps everything together and selected, so that they are moving together, but Inkscape looks for the center of the objects rather than the center of the group. Also, when you grab something to drag the former group, you must grab object 1. As long as everything is still selected, everything will move together, even though you only grab object 1. If you grab object 2, or any other object in the group, Inkscape will try to snap the center of whichever object you have grabbed.
So for clarity
1 - snap control bar like attached
2 - ungroup but don't deselect
3 - grab onto object 1
4 - drag so that the appropriate centers are coming close enough to each other (if the objects are odd shapes, maybe click twice on them before you start, to get a mental picture of where the centers are, to make sure you are dragging close enough to each other)
5 - maybe re-group the selected objects, if you want to make sure they stay together later
Any luck?