She went through the terrible loss of bereavement...probably she had been somewhat bamboozled by her son's behaviour.
She may have tried to keep the family together, as there was some disbelief amongst Jesus' siblings.
As for a focus of prayer?
Nothing in Scripture leads me to that conclusion.
From what I've read of church history, Mary seems to have been promoted by those who felt a substitute for the mother goddess was needed, and elevated Mary, without any real Scriptural evidence, to fit the bill.
Early statues of theMary with the infant Christ bear a striking resemblence to similar statues of the Egyptian mother goddess Isis, nursing the infant Horus - a couplet which had been Hellenised, Romanised, and spread as a 'mystery cult' throughout the Empire in thefirst three centuries AD.