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I am sorry to hear of this difficult situation.
While I don't know you, or the mother or any of the facts, knowing just what you told me it is not likely that you will be able to have the six month old child for two full weeks at a time.
Firstly, even if the child was much older courts will not want to have a child will be on such a disruptive schedule. There are good reasons why in a shared custody situation the child is with each parent for one week of the time. Second, it is not likely that a six-month-old baby would be expected to be away from a mother for anywhere near that length of time. Third, as a child gets older this type of schedule may be very difficult in terms of working out after school activities, lessons, and even attending regular school functions.
It may make more sense for you to consult directly with a family lawyer face-to-face so that you can gain a better understanding of what may be feasible in your situation.
I am sorry that is not the answer you were hoping for.