Reverse osteotomy to make the nose wider

You can have osteotomies and spreader grafts placed.  That can widen the nose.  The cartilage can be septal cartilage if you still have some.

The bones can be fractured and pushed out.  These must be held in place while they heal.Find a board certified plastic surgeon who performs hundreds
of rhinoplasties and rhinoplasty revisions each year. Then look at the
plastic surgeon's website before and after photo galleries to get a
sense of who can deliver the results. Kenneth Hughes, MD Los Angeles, CA

If the nasal bony pyramid, the bone on the side wall of the nose, was pushed in too much, osteotomies can be re-performed and the segment pushed outwards.  Such maneuvers can be frustrating as the bone has a tendency to return to where it was first located, so placement of some form of splint early on can help.  An alternative is onlay grafting to provide the impression of the bone being in the optimal position.  Please seek guidance from a surgeon experienced in revision rhinoplasty.

By reverse osteotomy, you may mean outfracture, which means moving the nasal bones outward instead of the usual inward (or towards the face). While this is possible, it is an unusual maneuver, and is used rarely. Basically the nasal bones or nasal bone is broken at the point where it meets the face and and is displaced away from the face. Situations that require this are usually facial trauma cases. Narrow noses from rhinoplasty are usually better treated with grafting techniques.