I don't want to hang out with a friend when she fights with her boyfriend
Why do you want to blow off your friend?
I don't want to hang out with her when she is in a bad mood.
It is good to stay out of a friends arguments. Wait until they cool down before trying to hang out.
I can't wait. She can be in a bad mood for days and I'm sick of being a backup friend.
If it takes days for her to calm down, then you should wait that long. You aren't obligated to deal with your friend if they are being nasty.