D.B.
Welcome to parenting the tween years. This is practice for the teen years, so you are wise to get a handle on it. Your 11 year old is starting to exercise her independence - a good thing. Except she's doing it by ignoring you - a bad thing. The younger child is emulating her, probably. Unless he's gotten away with more stuff as the "little one" and she's emulating him. Doesn't matter, really. The answer is the same.
You've learned that yelling doesn't work. Good. You've learned that 3 warnings is one thing for a 3 year old, and totally inappropriate for older kids.
Take comfort in the fact that you have not lost control. You have yielded control to them, and you just need to take it back. You have a few days of school vacation before they go back, so now's the time for a sit-down. Call it New Year's Resolutions, if you want to, but remember that resolutions are often just wishes and not rules.
Take today and write a list of every single thing your kids want. Make a sheet with 3 columns: daughter, son, both. Every single time they ask for something (make me breakfast, drive me to Julie's house, get me a snack, buy XYZ at the supermarket, wash my good jeans...), write it down. Put a star only next to those things they asked for politely, with a "please" and no attitude. If they do anything without being asked, write it down and star it (making a bed, picking up toys...) Then write down the stuff you do without being asked: 3 loads laundry (washed, dried, folded, put away), walk the dog, prep school lunches, empty the trash, clean the bathroom, write out the grocery list, drive a carpool already arranged, dinner prep, table set, dishes cleared, dishes done and put away, grocery shop/unload/put away. Write down stuff you had to do to provide safety or peace in the house (referee or redirect an argument to quiet it down, remind them to put on a seatbelt, shut off the overflowing sink, move the bikes out from behind the car...)
Now, change your attitude. Short of "paying the mortgage" and "driving to the doctor," everything on that list is something you are willing to do in exchange for appreciation and cooperation. Inform them that, come Jan. 1, none of it will be done without A &C (appreciation and cooperation). You can assign jobs, or have them pick. They can trade if they do it quietly and you don't have to referee. Between the review of the lists and Jan.1, inform them you will be available for lessons in the assigned tasks: how to load the dishwasher, how to do laundry, how to sort the recycling, how to make a sandwich and clean a lunch thermos, how to clean a toilet...)
Starting Jan. 1, they aren't getting stuff on their "ask" or "expect" list unless they do the chores assigned. No rides to Julie's house, no friends over, no playdates, no going to birthday parties (with a purchased gift), etc. That doesn't mean that they make a bed and then you have to do something for them. None of that - just refer them to the list you're already doing. You can post a list for school by the door if you want, showing contents of backpack and a general homework reminder, lunchbox, etc. They are responsible for this. Put a basket or bin for each kid, and pitch all shoes, gloves, toys and books into this. They can be responsible for finding their own stuff. Laundry? You are no longer doing an emergency load just because someone left their favorite shirt or their soccer uniform on the floor or under the bed. If they go to school with a wrinkled shirt or missing some homework, they can survive. No one gets kept out of college because they had to miss recess for a skipped assignment, you know? Let them incur the consequences NOW.
The trick is to stop fighting and start managing. You hold all the cards, You really do. You just have to stop any concerns that you'll be seen as a "bad mom" if they go to school in a shirt they wore 2 days ago or without a homework paper or permission slip. You have to not care what they say about you to their friends. You have to care much more about giving them life skills and responsibility. Do not relent. Do not complain if a job isn't done exactly as you would have. They still need you in other ways, as a counselor and advisor - that doesn't mean they need you as chief cook and bottle washer. Your job is to teach them, not be Ms. Popularity. When it's time for your kids to get a learner's permit or to go off with friends without adult supervision, you will be very happy that you endured their eye rolling now and created self-sufficient, capable, responsible decision-makers.