Congrats on the baby! The only advice I can offer is allowing this baby to become a confident bird. Allowing time to sit back and take in all in. The home's Family dynamic from noise to activity. A preferred place would be in a central location so this bird see's and hears the daily interaction of the Family or so called flock.
As for hands on my suggestion would be knowing that birds will test, they will nip they will bite. When is the question, and eventually finding out the triggers. Just because it'a a baby means nothing as to behavior and nipping or biting. Blue Fronts are one of the hot Amazons. They are not as laid back as the Red Lored, The Lilac Crowned, White Front or Mealy.
One suggestion on care and feeding to be all involved. If you allow the kids to put the food and water in rotating who does this chore as to everyone being involved. Not having one sole caretaker allows for your bird to see it's everyone who's the one who brings the good stuff.
Little kids can run, scream in play and this could set off the bird in a negative way so be prepared for this. One one should become this birds favorite if the Family interacts socially giving this bird the time and communication of talking to or playing with. Birds will try to choose their favorite mate so to say. It can happen, just knowing this allows for no hard feelings. The 4 year old and 7 year old will have interest, but not as much as the Adults for day to day care and interaction.
And by all means do not allow that bird on their shoulders to handle, you do not want a bite to happen on their face or near eyes. It takes time for everyone to figure each other out. A busy Amazon is a happy Amazon allowing all the fun toys for enrichment, foraging and chewing. Amazons are also not the needy kind of bird, they are great at self entertainment too.
Eye pinning and tail flaring are signs of excitement in both good or bad. Talking will also get an Amazon to pin their eyes too, it's not a bad thing just a way they communicate their emotions.
Best of luck, post pictures for us and by all means ask away if you have any questions. I am not a Blue Front owner, I have the lesser of the hot Amazons.
@melissasparrots is also another good Amazon Momma as well as
@Clueless owning two of the Blue Fronts.