EEA2 REFUSED- Reapply or appeal?

I'm an Italian citizenship living in the UK since 06/2016 and I'm a qualified person, an employee working since 06/2016 in London.
My wife and I have a 7 years old son. We moved from Brazil to London since last year. We are living together for more than 8 years.
My wife (unmarried partner) is 8 months pregnant and had the Residence Card refused. The home office is saying that we don't have proof that we are living together.
She is Brazilian and her tourist VISA is already expired. The home office didn't return her Brazilian passport and is asking to her leave the country. We have to call the home office to ask her passport, but, we don't know if it's a good idea.
We are totally sad and we don't know what we can do.
Someone, could you help me?

She is not your wife if you are not married.

For an unmarried partner, you should provide evidence of cohabitation for 2 years to prove durable relationship.