IMO the critical period ends about 8. multiple studies show this. so she has some time (2-ish years?) to try and regain vision in that eye.
why it was never picked up is an easy answer...b/c the pediatrician's office doesnt know jack about eyes, to be blunt. you would have had to seen an eye doc to diagnose that.
the reason you cant find a "straight" answer is b/c there are as many opinions on who needs surgery/treatment for this kind of disorder and who does not as there are doctors out there. there is no rule that says "X amount of amblyopia at Y age should be treated, but K amount of amblyopia at P age should not".
here's how i would treat it: if she can see better than about 20/100 at any distance with any lens, then IMO it might be worth trying to save the vision in that eye with surgery, progressive add glasses (or multifocal implant) and patching. if its worse than 20/400 at all distances, IMO its probably not worth it...she doesnt have enough time to make up the difference. 20/200-ish would be a grey area. it would depend on my perceived parental motivation.