what if she ask me to go shopping, should I just say no that I already took care of it?
yes. Don't wait for her suggest shopping, Don't wait hoping she'll suggest. don't worry that if you shop without her and then she wants to shop with you, you'll have made a mistake.
You were planning to take you D somewhere. W decided to come along, then decided to change the day because of the weather?
Is D with you right now? If so take her anyway. Just text W and say that a little rain can't slow you down or ice cream is needed on a day like today. DON'T say you're welcome to come or whatever.
You will slowly detach and get to a point where you don't factor in W's opinions, wishes, or what you think she might want to do into your decisions. The sooner you get to this point the better. Because first you will feel so much better about yourself. And second she will notice.
In the meantime you have to step back even if it's the last thing you want to do. If you feel like sending an email or text WAIT. send nothing for 24 hours. Post it here sleep on it and see how you feel later. It will save you weeks of heartache by not doing something rash.
