The extract in the question is E. P. Coleridge’s 1938 translation of lines 566–570:
εἰ γὰρ γυναῖκες ἐς τόδ᾽ ἥξουσιν θράσους,
ἄνδρας φονεύειν, καταφυγὰς ποιούμεναι
ἐς τέκνα, μαστοῖς τὸν ἔλεον θηρώμεναι,
παρ᾽ οὐδὲν αὐταῖς ἦν ἂν ὀλλύναι πόσεις
ἐπίκλημ᾽ ἐχούσαις ὅ τι τύχοι.
Euripides. Orestes 566–570. Perseus Digital Library.
Coleridge’s translation is literal, not idiomatic: it follows the original very closely and is probably intended as an aid to construing the Greek text.
As for the meaning, recall the dramatic situation. Orestes is justifying the murder of his mother Clytemnestra, in revenge for her murder of her husband Agamemnon. Orestes says that he has done a service to all of Greece, for if Clytemnestra had been allowed to get away with killing her husband in revenge for his murder of their daughter Iphigenia, then soon other women will be murdering their husbands “on any charge whatsoever”.
There are a couple of difficult phrases:
“taking refuge in their children” — this means, “appealing to their children for protection from the consequences of their actions”, as Clytemnestra had appealed to Orestes.
“hunting down pity with the breast” — an anonymous 1846 translation renders this as “hunting for pity by baring their breasts” which is much clearer. Clytemnestra had appealed to Orestes not to kill her, by baring the breasts with which she had nourished him as a baby. This refers back to lines 527–529 of the play:
Τυνδάρεως ἐπεὶ τίν᾽ εἶχες, ὦ τάλας, ψυχὴν τότε,
ὅτ᾽ ἐξέβαλλε μαστὸν ἱκετεύουσά σε
μήτηρ
Tyndareus Wretch! Had you no heart when your mother was baring her breast in her appeal to you?
Euripides. Orestes 527–529. Translated by E. P. Coleridge (1938). Perseus Digital Library.
For a more idiomatic English translation of Orestes, try Philip Vellacott’s, which renders this passage as follows:
As for your demand
That I be stoned to death, my answer is that I
Am a benefactor of all Hellas. For if wives
Grow bold enough to kill their husbands, and then fly
For refuge to their children, snaring their soft hearts
With bared breasts, husband-murder will become a sport,
Excused by any trifle.
Philip Vellacott (1972). Orestes and other plays, p. 319. London: Penguin.