Borders are always attached to the prints: they will never disconnect.  So you only have to worry about that if you are using photo mats since the mat sits under the prints: for photo mats, just make sure you select the mat(s) and not the print(s) if you want to move them.  On the main live view, you can select multiple prints and then click and drag on any that are selected.  They'll all move together.

Regards,
Mike

Don't select all because that selects the prints too.  Just select all the mats (individually) without selecting the prints on top... and then move by dragging any of the selected mats.  Think of them like placemats: you drag the mats to move them (and all the plates/silverware on them move with the placemats).

Mike