Whoa---hold on. If all of you live together as a family but you are not legally married then only one of you can claim the child. The other parent just has to file as Single and not enter anything about the child on their return.
You are trying to use a rule that is only for divorced or never married couples who live apart and share custody of the child. You do not "split" the child related credits if all of you live together. You do not say you have a signed agreement or a Form 8332 if you live together as a couple with your child.
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