Because the 'al' in Al-Qaeda is part of the terrorist group's name, I would capitalize it. However, the 'al' in Al- Qaeda is capitalized and not capitalized in many publications. 'Al' is an Arabic word that usually translates to the English word 'the' although 'al' never stands alone and is always a prefix to another words.
The question as posed is awkward. There is no violence between Iraq and al-Qaeda, rather there is violence perpetrated by al-Qaeda in Iraq and countered by the Iraqi Army, the Peshmerga, other militias, and, formerly, the US-led coalition. Al-Qaeda violence started when al-Qaeda members poured into Iraq midway through 2003. It has not ceased.