HH,
Just to correct you slightly, the UAE government does not support jihadists, or indeed Islamists of any flavour. Even the Muslim Brotherhood is banned there; it is one of the most aggressively secular governments in the region. I think I read somewhere that the UAE government has been piling pressure on the UK to publish last year's Jenkins Report into the activities of the Muslim Brotherhood in the West.
A good case study of the 'sides' we are dealing with is Libya, where Egypt and the UAE are backing secular forces while Qatar and Turkey back the Islamists. Picking out the Saudi involvement can be tricky because their government line can stray towards the secular, even while the private money and clerical hierarchy backs the religious.
It is indeed a snake pit! I think you can simplify matters when you reflect on who our traditional allies in the region are - Kuwait, Bahrain, UAE, Oman. Funnily enough, the ones that enjoyed British protection after the fall of the Ottoman Empire. Anyone who thinks the Saudis are our allies does not know their history.