The fact that you actually realize you are having anger issues means that your problem is about 75% solved already ;)
You just gotta put yourself in check, take a breath, ask yourself if getting mad, upset, mean or whatever is gonna make you feel better? I'm sure the answer will be NO.
I'd sit the 9 yr old niece down and have a woman to woman talk with her... she can be your best ally since she's 9 and can be very useful to you. Treat her like a big girl, and then expect big girl behavior from her.
You coddled them a bit too much in the beginning maybe, but it is not too late to change the game plan. They live in your home, you are the acting parentals.... so parent them, dont cripple them by treating them differently out of pity.
Everyone should have their chores and you should have your quiet time for yourself every day. I used to call it "my hour of silence". And everyone knew to leave me alone and not ask me anything for an entire hour.
You are hormonal, that's part of the 25% left in your anger problem.
You will be okay, just get a grip.... have a cup of tea. Stress rubs off on everyone in the household, don't be contagious.