Your retirement plan contributions are not deductible as such since they can only be applied to business income. If you were self-employed, you could deduct them from your self-employment income, but since you don't have any income associated with your household employee, the SIMPLE plan contributions are not deductible. You can't write them off against your personal income.
If you pay the household employee for child or dependent care, you can add the SIMPLE plan contributions to your expenses for purposes of the child and dependent care credit.