The order of these children is unknown to me.
The Barkers were yeomen farmers in England: a class of small freeholders who cultivated their own land. After Richard's death, it is said that his sons frittered away their inheritance, which is why they decided the best plan of action was to come to New Zealand to make a new start. The boys emigrated first and settled at Puhoi where they became successful farmers.

Source: Cherry SWAYN