Hi!! Congrats on your first cruise. You will love it! You have never been so pampered in your life.
Not sure what all you know or have read up on but the dress is casual all day, dinner is more dressy. You will have at least one formal night. You will see people dressed to the max. We choose not to dress up that much, I normally wear dress slacks, dress shirt and a tie (no jacket for me most times) my wife normally dresses a couple of steps above her Sunday best.
While around the ship easy on and off shoes are suggested as you will probably be by the pool a lot. A comfortable coverup for your swim suit will prevent you from wanting to change when you decide to go strolling on the ship although you will see people all the time is just swim suits.
Your children may or may not get hooked on Camp Carnival. We took our granddaughter 2 years ago (she was 11 at the time) and she had no interest in Camp Carnival 90% of the time, she just wanted to hang by the pool, talk to friends and slide down the slide. At that age you can give them permission to check themselves in and out of Camp Carnival. Trust me on this - you do not have to concern yourself with your children all the time - they are fine (unless you have misbehaved children that you are afraid to turn your back on LOL).
The food is to die for. Although we have not been on the Freedom (going in September) ALL the Carnival cruise ships we have been on have the best food I have ever had 5 star dining.
Hope this has helped you some. I know I did not tell you everything to pack but my wife always packs more than she needs. I think all you need is a bathing suit and a pair of flip flops!