。
She parted with her friend in tears.
Literal
She [topic-は] tears amid [manner-に] friend [with-と] parted.
涙ながらに (なみだながらに) is a set adverbial expression meaning 'in tears, tearfully.' The ながら here is not the simultaneous-action ながら but rather a literary form meaning 'amid, while in a state of.' 別れた (わかれた, 'parted') takes と for the person parted from.