i really pity u.the woman should not have shouted at u in the first place.shows how uncivilised she is....i admire ur patience throughout the commotion.
from my past experience werking in fine dining.here are some measures i could recomend to cool things down in cases of spillage.....
firstly....apologise in a sincere manner.just once would do.
secondly,offer wateva napkins or clean cloth nearby....as for ur cases maybe some soaked tissues would do(in foodcourt)
thirdly,offer something in return....(like bribe ehehe) pay for their food,buy drink.wateva u can afford.
once situation have calm down...offer to wash the stained clothes/buy them a t-shirt etc dryclean for them
if they say nevermind,then lucky u...just put a smile on their faces back,& i sure it will to urs too.....
just my humble peace of advice.....