Unless your family court order specifies to the contrary, you have the right to utilize qualified adults to assist you in child care. Presumptively, relying on a licensed teacher for such assistance is not unlawful and is unlikely to trouble the family law court. But, let's get real. Your wife is concerned that you and your girlfriend are having sex in the presence of your child. That's a very different situation and raises very different legal issues and risks. You won't have much success dealing effectively with your problem if you clean up the issue artificially when seeking advice and assistance.
You and your girlfriend need to talk with a skilled and experienced family law attorney. You are at risk for some serious concerns by the family law court and your child's mother may be in a position to make real and significant trouble affecting your girlfriend's employment and state teaching credential.
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