Question: What determines when we re-incarnate, and come back into this world and suffer?
The origin of everything is God. Every soul has come out of God, like a spark. The acquired habits of the mind determine when and how one re-incarnates.
The world appears good or bad to you, depending on your mental attitudes. The aim of all spirituality and religion - every religion is very respectable and worthy - is basically that the mind needs to become settled, and then it becomes more elevated. One day, if one could lose all the imaginations of the mind, if the mind can become completely clear, then it will merge with God as it is ultimately a spark of that Divine. If the mind becomes totally clear, then it will merge with the Divine, and won't come back.
You are looking only for peace and happiness. This world has unhappiness only ultimately, and so God is the recommended goal in this search. This world has fear and tension - today might be okay and happy, but tomorrow you might not be happy. So if we want happiness that is permanent, then we must find that which is permanent, which is God.
Question: At that stage where one merges with the Divine, can one choose to come back to this world?
Yes. Coming back is then a choice, where as before that, it happens automatically. If you want to help others, then you may come back.