S.D.
We've been traveling with our 3-year old very frequently since he was 2 months old, so we're old pros at this.
You are not allowed to carry on liquid in a container that is bigger than 3 ounces, and all 3-ounce bottles need to fit in a quart size, clear bag. You take the plastic bag out and put it through security separately. Breast milk and regular milk can be brought on in a bottle or sippy cup and must be put through x-ray separately too. Security may ask to open the cup or bottle to smell what is in there (but they never did that to us). I've also found that when my son turned 1 and could drink whole milk, that it's hard to find whole milk once you get past security (except for Starbucks).
You will also be required to take the shoes off your kids (even the little one), so be prepared for that. Just get to the airport as early as you can, so you don't feel rushed.
I hope I've answered all your questions. It all seems like second-nature to me these days, so I may have forgotten something. If you have any other questions, please don't hesitate to ask.