Forget about 8332 if you all live together as a family. That form is used by divorced or never married parents who live apart and share physical custody.
Since all of you live together, only one of you enters anything about the child on a tax return. The other parent does not enter anything at all about the child on their return. That parent files as Single.
It is usually better for the one who earns more to claim the child and use Head of Household filing status, and they also get EIC, child tax credit and childcare credit.
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