I suppose this sentence means that he decided to dedicate his entire life or some period of his life to supporting his brother's children. The reasons for such a decision can be different. For example, his brother might have died recently and in order to help his children grow up and mature he intends to provide any kind of support for them he can.
"She committed herself to the work of God"
Sounds like something said about a very pious person with strong religious convictions who has decided to forget about all carnal desires and spend most of his time praying and taking care about monasteries, the poor, and the sick. In other words, what is called mercy and charity.