The God of the Old Testament was not in the habit of ignoring things he didn't like. In verse 18 it is recorded that Menahem did evil in the sight of the Lord. After Verse 17 records that he reigned as King of Israel for ten years. Also, nowhere is there any record of any punishment for Menahem's deeds. Furthermore, note that Menahem was King of Israel and that the account in 2 Kings is written from the point of view of the Judeans.
Similar condemnations are present elsewhere in the story in reference to other Israelite Kings.
Once again the footnotes for this Psalm help us to understand what the author wrote. This psalm was written after the return of the Jews from Captivity in Babylonia. Actually, it was written during the Exile. At least, it depicts the laments of the Jews during the Exile as they awaited their return to their homeland. The psalmist is personifying the city as a mother whose little ones are the adult citizens, not the infants, of the city.