The Collaborative International Dictionary of English v.0.48:

Embroilment \Em*broil"ment\, n. [Cf. F. embrouillement.]
   The act of embroiling, or the condition of being embroiled;
   entanglement in a broil. --Bp. Burnet.
   [1913 Webster]

WordNet (r) 3.0 (2006):

embroilment
    n 1: an intricate and confusing interpersonal or political
         situation [syn: imbroglio, embroilment]

Moby Thesaurus II by Grady Ward, 1.0:

181 Moby Thesaurus words for "embroilment":
   action, ado, aerial combat, affray, agitation, altercation,
   argument, armored combat, battle, battle royal, bicker, bickering,
   blood feud, bluster, bobbery, boil, boiling, bother, brawl, broil,
   brouhaha, brush, bullfight, bustle, cacophony, chaos, churn, clash,
   clash of arms, cockfight, combat, commotion, conflict, contention,
   controversy, conturbation, discomposure, disorder, dispute,
   disquiet, disquietude, disturbance, dogfight, donnybrook,
   donnybrook fair, dustup, ebullience, ebullition, eddy,
   effervescence, enmeshment, exchange of blows, excitement,
   falling-out, fanaticism, feery-fary, ferment, fermentation, feud,
   fever, feverishness, fidgets, fight, fire fight, flap, fliting,
   flurry, fluster, flutteration, foment, fomentation, foofaraw,
   fracas, fray, free-for-all, frenzy, fume, furor, furore, fury,
   fuss, ground combat, hand-to-hand combat, hand-to-hand fight,
   hassle, helter-skelter, house-to-house combat, hubbub, hurly-burly,
   hurry, hurry-scurry, imbroglio, inquietude, involvement, jitters,
   jumpiness, logomachy, maelstrom, malaise, melee, moil,
   naval combat, nerviness, nervosity, nervousness, open quarrel,
   pandemonium, passage of arms, passion, pell-mell, perturbation,
   pitched battle, polemic, pother, quarrel, racket, rage, rampage,
   restlessness, riot, roil, rough-and-tumble, roughhouse, rout, row,
   ruckus, ruction, ruffle, rumble, rumpus, running fight, scramble,
   scrimmage, scuffle, seethe, seething, sharp words, shindy,
   shoving match, skirmish, slanging match, snarl, spat, squabble,
   stand-up fight, stir, storminess, street fight, strife, struggle,
   swirl, swirling, tauromachy, tempestuousness, tiff, to-do,
   trepidation, trepidity, trouble, tug-of-war, tumult, tumultuation,
   tumultuousness, turbidity, turbulence, turmoil, tussle, twitter,
   unease, unrest, uproar, upset, vendetta, vortex, whirl, wildness,
   words, wrangle, yeastiness, zeal, zealousness