The suture site on right eyelid opened up. Any suggestions? (photos)

I would have left the dehised would alone.  They close fairly rapidly on their own and generally do not warrant surgical intervention.  Some believe this is a sign of an infection or some issue.  As mentioned this often clears up on their own with minimal would care in the form of antibiotic ointment.

Wounds will sometimes open for up to 10-12 days after a surgery.  Although it may look bad initially, it should heal well and without any significant scarring.