I'm annoyed at my fathers girlfriend
Is there a reason you are annoyed by her?
I'm sick of her. I can't stand her.
You can tell him, but beware of the consequences. He may not take kindly to you saying that.
I think my father can handle it, he's not too easily upset, I want her gone.
As long as you will be able to handle the consequences. He may not like what you have to say, but sometimes being honest is the best.