You shouldn't go out.
If you leave your own home, whether rude or not, it just delays the inevitable time that will come when you have to face this.
Don't let her think that she's so bloody important that she needs avoiding, because she isn't and she doesn't.
Welcome her to your home, be bright and breezy. You have the upper hand, you're on home turf. If she makes hurtful comments, politely but firmly call her out on them, Good responses above.
She will be in your life, so you need to change to deal with this. Detach mentally, so she's not crowding your head. Be proactive, assume she'll be ok, pick her up on it calmly and politely if she's not. If you act rationally and politely, you'll show her poor behaviour up.
Don't avoid her. Stop thinking she has power over you. She doesn't and she never will. But you must be you, put her in her place if need be, and let her know that her words no longer affect you.
If you go out, your giving her a strong message that she intimidates you. Don't give her that message. She needs to know that her presence in your home hasn't caused a ripple.