non-EEA mother with EEA child

[johnnymotel]

I'd like to know how this one works?
Sister of my wife is wanting to marry her BC boyfriend. She has a child from a previous relationship and that child has Italian nationality. The mother is Brazilian.
Does she have to follow the usual entry visa routes laid out for non-EEA citizens or does the child make it possible to enter under EEA rules.
I've tried reading the usual documents but couldn't really fathom this one out.
I suspect she will be treated as a non-EEA application, but then will the child require an EEA application and will the BC partner have to prove his income sufficient for just the mother or mother and child?

[Obie]

The child will not need to meet the financial requirement, if it can be shown that he will be a qualified person within the meaning of the Chen Ruling upon entry, following the initial right of residence.

The mother has the option of applying for spouse visa, or apply for EEA family permit as the Primary carer of an EU child, provided the requirement of sufficient resource and a Comprehensive Sickness insurance is met.