I get so frustrated that I'm always yelling at my family when they make me late to things.
Why does your family make you late for things?
They are always so slow to get ready, it makes me angry.
People are expected to be on time for appointments. You could tell them you need to be some place earlier if you know they are always late.
I've tried to tell them, but they still don't change their ways.
It's hard when people are not considerate. Try to tell them how upset you feel when they make you late.