Heys nickle,

I am not sure what state you're in, but this is from the victorian government:

Working with Children Check
In 2006, the Victorian Government introduced a new checking system to help protect children under 18 years of age from physical or sexual harm.

The Working with Children (WWC) Check creates a mandatory minimum checking standard across Victoria. The WWC Check helps to keep children safe by preventing those who pose a risk to the safety of children from working with them, in either paid or volunteer work.

If you work or volunteer with children you may need to apply for a WWC Check. Employers, volunteer organisations and agencies must ensure that any of their staff or volunteers who need a WWC Check have applied.

Everybody who requires a WWC Check must have a WWC Check or have applied for one by 30 June 2011.
From this, I would take it that the decision as to whether or not the aide requires a WWC check is not that for the mother of the child to decide, as you have so very correctly stated, there are more than just her child in the room.

Also found this which sorta agrees with the mother of the other child around the being directly supervised, but as she will be working regularly this is void:
Who Needs to Apply
Under the Working with Children Act 2005, only people engaging in ‘child-related work’ must apply for and pass the Working with Children (WWC) Check. Not everyone whose work brings them into contact with children will need to apply for a WWC Check.

You need to apply for and pass the WWC Check if you meet all of the following criteria:

your work or volunteer role involves contact with children in connection with one of the 20 listed child-related occupational fields
you volunteer or do this work on a regular basis
you have direct contact with children under 18 years of age and are not directly supervised
you do not qualify for an exemption from the need for a WWC Check.
Then there's this from the list of 20:
Educational Institutions

Educational institutions for children, specifically:
• State Schools (including all primary, secondary, technical and special State schools)
• Non-Government schools (including all primary, secondary and special non-Government schools)
• TAFE colleges and TAFE Divisions of universities providing VCE and/or Victorian Certificate of Applied Learning (VCAL) subjects
• Some adult education providers providing VCE and/or VCAL subjects
• Other institutions providing children's study or training programs
I would be talking with the teacher / principal and clarifying with them as opposed to the mother(s).