Spouse Visa - Sole Responsibility

Hi, I’m sponsoring my wife for a spouse visa and also two children as dependents.  I am the step-father.  My question relates to the supporting documents to show sole responsibility for the children’s upbringing. 

Can anyone who has made such an application please let me know what kind of documents/evidence they have provided?  Is it just letters from schools, doctors?

Thank you

Best is a copy of the custody agreement and a letter from the father stating he has no objections to them moving overseas.

Is the father still in the children's lives?  If not, it starts to get a bit more complicated...