http://www.strabismus.org/amblyopia_lazy_eye.html
When a child is diagnoised with strabismus, the first thing doctors recommend is physical therapies that try to condition the two muscles one each side of an eye to get the eye straight.
If you have tried that and it did not work, then you need to consider surgery. I don't want to scary you, but such surgeries may be nessary since uncorrected strabismus may lead to amblyopia, reduced vision in one eye. In addition, serious strabismus will stay for life.
The procedure is simple. The doctor may decide to operate on one eye at a time so that during the recover period the child can still see the world. For each eye, a single cut is made at the inner corner of the eye (not on the eyeball) to tighten the muscle. The patient recovers his consciousness in a couple of hours and can be taken home with the eye covered. A doctor visit a few days later will check the recovery and adjust the sutures. At this time the gauze is taken out and the patient can practice looking at things (usually he will see double images at first but it will go away). After another week or so the suture is removed. There is essentially no visible scar afterwards.
Sometimes the correction made is not exact, and occasionally you will notice slight strabismus in the eyes, especially after the child gets tired at night. This should not be noticeble to an outsider who is not aware of the pre-existing condition.
I wish both of you can avoid the surgical solution; in any event, you have my sympathy with you because I have been there.