I agree with everything B said. My son was pretty much a peach throughout two and then, whoa! Three came and it was like I got a whole new kid. What's worse, one with behaviors I didn't particularly like.
Some ways of coping:
Stop asking questions as much as possible. I eliminated a lot of verbal choices for my son. Sometimes, his brain was trying to catch up to what I was saying and it would feel like a year was passing.(and kids can be like deer in the headlights when asked questions). I started making the choices for him, or in some instances, offering choices through presentation. (Example: Instead of "do you want peas or apples" just putting both on the plate in small amounts.) I put my son's clothes out-- picked them out for him. No "do you want the truck shirt or ..." If he wasn't proactive about his opinions, then I wasn't going to ask.
Regarding circle time; at this age, I would often offer a quiet alternative to my preschoolers. who didn't want to sit in the group.(I'm a preschool teacher on hiatus.) They could quietly look at a book or do a fine-motor activity (lacing beads, connecting foam pieces, puzzle) as long as they didn't disturb the group. If you look at the NAEYC's (National Association for the Education of Young Children) Developmentally Appropriate Practice handbook, this *is* appropriate to *not require* a Three to sit at circle; it is appropriate to provide suitable alternatives. I think sometimes, some programs run a circle time which may be too long for some in the group. They need lots of breaks between sitting quietly to wiggle, participate, sing, do dances and fingerplays or play instruments, or act something out. So, I would look into that, ask to come and observe during that time. Circle shouldn't just be about passively listening only.
Cleaning up toys--don't want to help? Then they go away for a while. Keep the number of toys reasonable and make sure there is an organized way to do this. She'll need help from you. I start simple: "Let's find all of dolly's clothes and put them in the basket." Be sure, at this age, that you are modeling this by doing it with her, not just giving orders. I generally did a lot of cleaning up until kids were about four or so, at least 40-50% of the work WITH them. And if she refuses, either try a hand-over-hand approach (your hand over hers, picking up the toys) or do make them disappear for a while.
Also, make sure she's getting enough physical activity during the day. We have rain gear at our house just to ensure it is possible to go out in rainy weather. (Here, it rains a lot.) Kids who are having a hard time being still may need a physical outlet. Think, too, about getting a small trampoline and having it available when you can supervise. IKEA also makes a great tunnel that you can set up and store easily. Kids love tunnels!
Being gentle/safe with her brother:that's non-negotiable. The fact of the matter --at least from what I observed as a nanny--is that younger siblings start to cause conflict when they become more mobile, often intruding on the older siblings' play areas or sense of space. Encourage your daughter to move her playthings up to the table, out of reach, and I strongly suggest making a few baby-free places for her. One family I worked with--we used the pack and play for the older child when she wanted to play alone with her Polly Pocket stuff/little pieces. Or a sturdy gate across a doorway can be a helpful thing, too. Separation is important, as is making sure she gets one on one time with you.
Know that you aren't a failure of a mother-- the ones who fail simply wouldn't have taken the time or had the insight to ask for help. Good luck!