I am Married but separated. My 2 children lived with myself and my wife from jan 09 - April 09. At which time we moved in with my mother in law for 2 months. I then left with 1 child who lived with myself for 6 weeks. Can I claim 1 child as my dependent when I file my taxes?

This is a basically the same as the other question you posted: https://www.askmehelpdesk.com/taxes/can-file-taxes-child-who-lived-me-6-months-last-year-457058.html

It all comes down to - which parent did the child live with the most during year (spent the most nights with)? That is the parent who is considered custodial, and is therefore the parent who can claim the child as a dependent.