No don't file the 941. Instead of withholding taxes (federal and/or state) and having to file W2s annually, 941s quarterly and state quarterly reports, don't withhold and just have your mother pay her quarterly taxes. Then when she does her tax return she'll report the income (you paid her) as wages not reported on a W2. She would also report the quarterly taxes she pays to get those payments credited on her return.
You can use the payments you are making to her a expenses for the childcare credit on your return.
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