Without knowing much more about his past history and meeting the dog, it is impossible to say safely what the problem is and how to fix it. As Jane says, look for an experienced trainer who can observe Max and your behaviour.
However, can you say what you mean by 'turning on us'. Is he growling, snapping or bitting? When does this happen? Is he protecting food, his bed, his toys, etc?
I have rescue cockers and also foster rescues, but would not be happy that a dog was snapping or bitting me after a month (I don't have children) without some very good reason. Growling, ok - it is their first line of defence but I would expect to know after a month what made the dog do that.
Dogs do take time to settle and if Max has been used to living with his old friend, on his own and getting his own way, he may take more time to re-adjust to his new home with a child. However, during that time, there may be a danger to your child - depending on what Max is doing, when and why.
Please give us more info, but as Jane says, only someone experienced and seeing the dog and you can really help with the problem.