You summarized it basically correctly. What is confusing you?
summaries serve their purpose. I sleep til 5pm these days and watch too much sports, then I see the possibility of 100k refugees, Saudis dropping bombs (possibly? potentially?) against US wishes. would they dare do that? wasn't the Iran deal the step forward toward "stability in the Middle East?" now the center-left commercial media is all afraid that the Yemen thing could get im the way from an Iran nuclear deal, the US is playing brinkmanship and sending over a fleet, etc... basically trying to bait Shia Iran into action in support of the rebels which would throw the nuke deal out the window.
all I really understand about the whole thing is you get these ultra-fundamentalist Shia groups fighting established Sunni gov'ts the US feels they can work with. Iran is troubleshome because it's Shia. I don't really understand that part of the world, except it seems more and more like a circular fck-up, largely owing to the vacuum created by Western intervention (give the Soviets their 5-10% share of the blame here if it makes you feel better. the rest is all on the USA)