It sounds to me like she must be getting praised at church and at her friends house for her good deeds - moreso than what she may be getting at home.
Unfortunately, just like how your family takes your everyday tasks & accomplishments for granted, you are expecting that things should get done by her without the need to make a big deal about it. Obviously, that's not working. Although I believe that all family members should have assigned chores, structured roles, and contribute their time without monetary compensation, a pat on the back, a "good job", and a "thank you" is essential when the chore is completed. It will also teach your kids to do the same when you do something for them.
In this case, punishment does not seem to be the answer, it will just create a bigger rift in your relationship. Also, by removing her from the positive activities she enjoys could cause larger issues in the long run. She could completely rebel and begin giving you REAL problems (sex, drugs, etc).
Instead, sit down and have a "heart-to-heart" and explain why you depend on her and that she is a huge help in your life. Maybe consider giving her more adult freedoms for every adult way that she helps out. Possibly start with 1 week where if she does all her normal tasks, she can do a special activity with her friends and continue that. Then, for every extra task she does out of the norm, you will let her curfew be an hour later than normal for a night. Or, let her decide to not do one normal task on a particular day. But most importantly, make sure you recognize everything she does that makes your life easier and helps the family. She is a teenager and needs your acceptance and her independence.
As far as cruel things that she sometimes does to her siblings, remind her that she is a role model to them and is not setting a mature example. But, also credit her when she positively influences them.
Another thing to consider is that since she is the oldest, you probably expect a lot more from her and probably have for a long time. She is not the mom and should be allowed to be herself.