My friend apologized to me after she didn't attend my wedding because her kid had a meltdown, but I'm not going to forgive her.
Why not forgive her if she apologized to you? That seems mean of you.
I want to make an example out of her this time.
While it is understandable to be upset with a friend for missing one of the biggest days of your life, if she had a good reason then you should consider forgiving her. You want to have close friends around and you shouldn't make them apologize for having lives of their own, because people will think you're rude if you act like that all of the time.
Nobody cares if I forgive her or not.
I'm sure she cares if you forgive her. If she apologized, she clearly wants your forgiveness and feels bad about what happened. Being a parent is difficult, so you should try to be understanding of the fact that sometimes her children will interfere with her schedule.