Start by combining the water and cranberries in a large saucepan over medium-high heat. Cook, stirring occasionally, until the cranberries "pop." Then strain and discard the seeds and skins. Allow the cranberry mixture to cool completely, you can pop it into the fridge if needed.
While the cranberries are cooling, heat the milk to 175° in a large saucepan. Then stir in the sugar until completely dissolved. Allow this mixture to cool as well before mixing in the cream, juices, extract, and cranberry mixture.
Last, fill the ice cream maker and freeze according to the manufacturer's instructions. I would suggest allowing the ice cream to firm up in the freezer for at least 2-4 hours before serving if possible.