I have a bezier curve, and a rectangle that should be attached to part of the bezier. Is there a way to move that part of the bezier and the rectangle together, without moving the rest of the bezier?

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Yes, there probably is a way to do this. But I just want to clarify the situation. You need to move the entire rectangle, and only part of the Bezier curver, is that correct?

To do that, you'll need to convert the rectangle shape to a path. Select it, then Path menu > Object to Path. Next, using the Node tool select both the rectangle and the Bezier curve. (If you hold the Shift key, you can make the multiple selection.) Using Shift again, next select the 4 nodes of the rectangle, and the node on the Bezier curve which touches the rectangle (or the one closest to it). Now you can grab any of the selected nodes and drag around the entire rectangle, and part of the curve . If you see that too much of the curve is moving, you could place new nodes to the Bezier, as needed.

Something tells me there's more to this issue, or there will be soon. But I can't quite perceive what it might be. Anyway, let us know how it goes

Your solution is exactly what I was looking for, and your intuition is very sharp.

Is there a reason I can't select both the rectangle's handles and my regular nodes simultaneously, without converting the rectangle to a path? Say, for example, that the rectangle is instead an arc. Once I have node-ified the arc, it is no longer easily manipulable. I'd like to be able to keep the object in its original form.

Ah yes. I was actually wondering about that. I don't know a way.....or at least I can't think of it at the moment. It seems like it should be possible, and I feel like I'm forgetting something obvious.....but I can't quite put my finger on it. Or maybe it's not possible.

Let me ask this though. Why is moving the object separately from the path, not possible? Why can't you move the object, then select the node and move it?

If the rectangle isn't located on some easily distinguishable landmark on the bezier path, it's extremely difficult to eyeball the proper position to move them one after the other, keeping them attached. You would have to use auxiliary lines to snap objects to the final position. Also, if you had to rotate and translate the objects together, placing part of the bezier in a specific position and the rectangle in another specific position, it's no longer possible to see both objects at once while you drag them around.