Mommy Is Embarrassed

So many times Ivy makes me proud~ when she uses new words, uses the potty, or plays well with a friend. This morning was not one of those moments. To be honest, I was down right, wanting to crawl in a hole and never come out embarrassed. Ivy has not been perfect- by any means- but she has been pretty easy. Sleeps good, eats good, and is overall easy... However, I would say as of the past 2 weeks (really since hitting 18 months) we are day in and day out into the terrible 2's. (A little early, I know....) I can handle tantrums, we isolate her, she calms down in time out, and then she is ready to go again but I don't quite know what to do with her aggression. That is where this morning comes in!
So we go to the library for story time and take a seat behind a mom, her little boy (9-ish months) and her daughter (4 yrs). Ivy likes to be in the front so after a few minutes she starts weasling her way between the mom and baby and the big sister. The mom says it is fine and Ivy is dancing and singing. She is happy! Ivy then is in full focus on the little boy's paci. Her "ba-ha-ba" is on day 6 of being in the crib.... not the car, not the church/gym nursery, no where but the crib. I hold her on my lap and talk about how babies have ba-ha-ba's and big girls only use them in the bed. She was back to singing about monkeys jumping on the bed when

STRIKE 1- She grabs the boys paci rears her arm back throwing it at him and hitting him in the head.

Mommy immediately apologizes and takes Ivy in the hall for time out. The whole way out she is saying "hit the baby, hit the baby." She sits in time out while I stand around the corner. Then I talk to her, say we are going to say sorry, we don't hit, it hurts.... blah blah... the whole deal. We go back in. Ivy signs "sorry" which is monumental- she usually refuses to apologize in any sense of the word. We are listening to a story about a moose and everyone is happy and then

STRIKE 2- Ivy decides to smack the older sister square in the head... hard smack... like makes a noise kind of smack.

I was about to die- literally. I apologized to the mom and child and wanted to cuss the other 45 sets of eyes who were staring daggers through me as if I put Ivy up to abusing this family on their trip to the libray. I packed us up and the whole way out she continued yelling "books, books." I didn't talk to Ivy the whole way home, instead I cried about what in the world I have done or failed to do in creating these aggressive behaviors. We came home, ate lunch, and I put her down for an early nap.

Now I sit here- reflecting on this embarrassing moment- and trying to figure out what my next steps as a parent are. I have went back and forth about how to discipline this behavior and what would be good for Ivy. What will help her control this aggression? What will help teach her social skills? I have been so sad and in the end I know I will have many more of these moments throughout Ivy's life. (Pay back is hell~ I am pretty sure I have embarrassed and saddened my mom many a times..... sorry, mom!)

Do you have strong willed child? Or know one? haha :) Any suggestions are welcome!