Hi jkp653. If she put you down as an alternate leader, then you can pick up the permit and hike without her. Picking up the permit is the critical part -- you must show ID there.
If she didn't put you down, only chance you have is to call the Wilderness Permit number 760-873-2483 and hope they agree with the "extenuating circumstance" situation. If they agree to add you as an alternate leader, then you can go without your wife.