Fun fact: Fakebook put me in fakebook jail for two days for writing that Princess Kate's hat looked like a saucepan lid.
My sister posted something that irritated me to the point that I took a Fakebook vacation by disabling my account, ( or whatever you do that doesn't delete it.) Sis and I don't agree on politics. I had intended for a one week vaca, but I stayed out for at least a month.
You were right to delete it, least said soonest mended is probably the way to go in cases like this.
It was petty, manipulative, and mean spirited of your sister and cousins to goad you into looking at something they knew would be hurtful. No amount of "well, you should know the truth" excuses this. None. I could go up to new parents and tell them, "You know, your baby is really homely" and it could be true. Telling them that is neither nice nor helpful.
A local news station used to have a tagline: news you can use. In my daily life, I sometimes consider whether the 'truth' on the tip of my tongue is useful to the audience at hand. Often it's not, and I shut up. You know this daughter is a drama-llama. Don't let your sister and 'friends' manipulate you into looking at this stuff.