I think you’ll find that sometimes those who are the most strident about religious rules and regulations/Do’s and Don’ts are the ones who latch onto the legalistic aspect of the faith because the spiritual side is so empty. There’s no doubt she cares about the children, but all her experience within the church has done is feed her suspicion and cynicism about human nature in general. She is quick to think the worst of Father Flynn and cast broad brushstroke judgments of others on superficial matters. Perhaps her “doubt” has to do with her belief in a God that could allow so much suffering and evil (as she sees it). Perhaps it is an admission that her Certainty is a mask for a fragility in belief that these events have brought back up to the surface. I don’t think she has any reservations about the moral righteousness of her position, but that righteousness seems, by the end, to be rooted in the Letter of the Law and not in something more profoundly personal and sacred.
I don’t think there’s any doubt that there’s some kind of skeleton in Father Flynn’s past, but I think the film still makes it quite ambiguous as to whether anything happened at that particular church–or even, in fact, at the previous one (for all we know, there was also an Aloysius at his last appointment, and he will always be doomed to run from something he did long ago, even if he is in control of his impulses, now).