Hi bri-82 .....
Not sure about the eyeball turning ...... however, many of us experienced double vision for awhile following surgery, which may be related.
I had significant gaze stabilization problems following both of my surgeries. Still having a slight problem occasionally at two months most recent post-op. If I change directions and look at something specific, sometimes it takes a second or two for it to "stop moving" and for me to be able to hold my gaze on it.
One of the exercises I learned from my vestibular therapist three years ago (following first surgery) was to put a large letter (used A) on a sticky note, place it on the wall at eye level, stand back about 5-6 feet ..... keeping eyes firmly focused on the letter, begin moving head slowly from left to right for 10 times, then up and down 10 times ...... gradually increasing speed of head movement without losing a firm gaze. I really need to go back and do that again.
The fact that you had facial weakness would also indicate that your AN side eye may be slower to respond until that weakness goes away.
Best thoughts.
Clarice