The payment of child support is to help feed and cloth your child; the division of community property has nothing to do with support (unless you have sufficient assets to divide that will produce income). So...absolutely! But she will get 1/2 only if the house was purchased during the marriage with all community property funds. Either party has a right to reimbursement for any separate property contributions to the house.
Please clarify what you mean by "claim half the house."
Do you mean claim half interest in the property? As Ms. Routledge says property rights have nothing to do with child support and everything to do with the nature of the funds used to pay for the house.
If you mean she is claiming the right to live in half the house that is another question.
Please provide more details so we can better answer. Thanks.
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