。
She is proud of her children.
Literal
She [topic-は] her own children's matter [object-を] pride [as-に] is-doing.
~のことを + verb-of-attitude is the standard frame for directing an attitude or feeling at someone, with のこと softening the bare noun into 'the matter of X.' Here 自分の子供たちのこと frames her children as the matter being held in pride — a slightly warmer or more inward feel than the bare 自分の子供たちを. 誇りにしている uses the [X]を[Y]にする pattern to mean 'takes X as her pride.'