My guess is that the SMLLC is Jim Smith, LLC whereas the tax return is for Jim Smith which does not have the LLC. The existing EIN should be used for employees of the regular business purpose of the LLC. A nanny to watch the kid is not a business purpose for the LLC.
I believe the client may need to get an EIN for themself as a person, not as an LLC. They may also need to register with the state as an employer.
I also believe you will have to get an EIN for self. Instructions for schedule H says, If you have household employees, you will need an EIN to file Schedule H. Here is link:
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