Even though Georgia is a no-fault divorce state, alimony is dependent on many things.  The length of the marriage and the disparity of income are just two of the factors.  It is possible that you could get alimony for a period of time until you get on your feet and can get a job making enough to suport yourself and the children.  You should also be entitled to child support which is generally statutorily governed.  "Leaving" with the kids can in some cases be argued as abandonment unless you have a reason for doing so.  You should speak with an attorney to determine whether your circumstances justify "leaving" and how much if any alimony/child support you could receive.