It is impossible that the allied powers should extend their political system to any

portion of either continent without endangering our peace and happiness.

This sentence gives a hint of a threat. I have to re-write the sentence and state the threat directly. Idk how to do that so please help!

We endanger our peace and happiness by trying to extend our political system to either continent.

Note that the second word in the above sentence is "endanger."

To directly state the threat implied in the sentence, you could rephrase it as follows:

"Our peace and happiness are at risk if the allied powers attempt to implement their political system in any part of either continent."