D.B.
My daughter had eye surgery when she was 7/8yo for strabismus (esotropia is a simular form). It was outpatient and pretty fast. Dr.s typically work on the youngest patients first thing in the morning so they aren't still around for half the day being hungry (there's a mandatory 8-12hour fasting that is easy to do over night - just don't give breakfast in the morning and you're set!). Given her age she wasn't the first one, but she was in just before lunch. Prep mostly included a bit of tape above the eye she was to have surgery on and (if i remember right) she was given one pain med to prep for surgery - get it into her system so she didn't hurt as much as she "woke up" - and that made her feeling silly and a bit clumsy. I was with her up until they wheeled her back to "smell the funny mask". The nurses were great and even asked her what flavor she wanted.
The first hour or two after the surgery are probably the roughest, because the stitches inside the eye are bothersome. My daughter was given some heavy duty pain killers at the clinic before being sent home about 3pm-ish. I rode in the backseat with her while hubby drove us all home although we did stop for milkshakes. She slept most of the rest of that day.
Had a checkup a couple days later and then again a 4 or 6 weeks (?) after that to make sure things were still ok. The stitches eventually dissolve and the irritation is gone by the end of the first week. My daughter's eye was red for a little over two weeks (all her classmates thought it was cool! lol), and whenever she did cry those first couple of days the tears were red tinted. Dr's orders were no swimming, stay at home and take it easy for those first two weeks.
I think the hardest part was hearing her actually wake up on the nurses (They wouldn't let me back there until she had spent a few minutes "awake" from the general anesthesia.) She's always been one to fight everyone unless I or her father is there to calm her and she literally came awake and screamed. I think we ended up staying an extra hour because she really worked herself up into a fit and they wouldn't/couldn't send her home until they had good normal vital signs from her (normal procedure).
We had done visual therapy for years... But she also has infantile/congenital nystagmus, so that really complicated every non-surgical intervention we tried to do. I would think if your daughter's case is severe enough, I would go ahead and opt for surgery instead of trying to spend so much time and effort on something that might or might not work.
feel free to message if there's other questions. hope that helps!