Eloise made a deal with Smokey by AJB

This may have been posted before: if so, sincere apologies in advance. Also first time posting, so people please be gentle.
Here goes:

I always wondered why Eloise left the island. We know Charles left because he broke the 'rules'. But why did Eloise leave? She was a 1/2 leader of the Others- and she would have become the leader when Charles left. We know that Ben took over instead.
So did Eloise leave before Charles was deposed or after? And more importantly - why?
Here's what i think happened: After 1970s Eloise discovered that she had killed her own son - she wanted to take it back - the idea was of course introduced to her by Jack but after they 'die' (like Richard pointed out to Sun in 'Follow the Leader'-" Yes i know all these people because I watched them die"), she doesn't know what to do. Maybe she approaches Jacob (or Richard) but is turned down. And this is where Smokey comes in - He offers her an alternative: the same Faustian deal he offered to the Losties. I'm guessing she took it. If she told this to Charles - he would probably be upset with her - and goes off to have ' a child with another woman'. Or he banishes Eloise off the island.
And she waits off the island to set the chain of events that will alter the timeline and create the ALT.