1) ''Subtlety'' means ''softness'' (''delicacy'') or ''discretion''. As for ''mallet'', it is a hammerlike, often short-handled tool with an enlarged head, typically of wood, used for driving another tool, as a chisel, or for striking a surface without causing damage. So, you should know that a mallet is not a subtle weapon at all!
In the sentence at issue, the writer is basically saying that ''Stern grieved over the fact that Pro-Israel groups used the document as a weapon.''
*NOTICE: The expression ''with the subtlety of a mallet'' is being used ironically to convey the idea that those Pro-Israel groups succeeded in using the document without anyone noticing or perhaps with discretion. Altogether, they managed to make use of the document.
2) The verb ''to chill'', in this context, gets the meaning of ''to moderate'', ''to make (something) less extreme'' or even ''to pacify (a certain situation)''. So, the last line could be rewritten like this:
''In November, Stern told the US Congress that enshrining the definition in legislation would make the 'political speech' of pro-Palestinian students less extreme.'' (If the US Congress should enshrine the definition in legislation, then the ''political speech'' of those Palestinian students would be less likely to create tension.)
Did you get the idea now?
Hope that helps!!!