This article (here) sums up nicely how the story unfolds: Basically, after Philippine independence, the Northern (Christian, Manila-based) Philippinos dominated and suppressed the Muslims, leading to bloodshed, retaliatory killings, and civil war. Groups dedicated to defending the Moros way of life and to battling against the Manila-based administration exist to this day, some (notably Abu Sayyaf) with purported ties to Al Qaeda. The conflict is not simple, and it is not one-sided.
The above cited article makes the case for mediation between the two groups, semi-autonomous status for the Moros, and development of the southern islands -- not military campaigns and cycles of retaliation.
Re-enter the United States, and this time it's not General Pershing and American doughboys in the jungle. That is so 1911. This time, it's combat advisers and drone strikes. Make no mistake about it: drone strikes are good at assassinating specific targets (read: killing people). They are not, however, good at solving a 400 year old political, social, economic and religious problem.
If the past ten years has taught us anything, it should be that we cannot kill our way out of a complicated situation.