
...a nice big Italian family.
You will need to go through three different consulates. Connecticut and NY will use the NY consulate. Your child living in Boston will apply there, and if your other child legally resides in New Zealand, he/she must apply there.
Probably the easiest approach is to have your husband apply first. Try to schedule an appointment for him and your three children who also live in the jurisdiction of NY. In this way, you will all be using the same qualifying documents. Once your husband's citizenship is recognized, your children and grandchildren living in the other jurisdictions should be able to apply by referencing their father's application. They may want to contact their own consulates to determine what specific information they will need and what documentation they must provide.
In terms of your husband's documentation, he will need:
His grandfather's Italian bc
His grandmother' Italian bc
His grandparent's marriage certificate
Death certificates for both grandparents
His grandfather's naturalization certificate
Note that US documents for direct line ancestors (except the naturalization certificate) must have apostilles and be translated.
He will need the same documents for both his parents and again his father's papers will require apostilles and translations.
Your husband, you, your children and your grandchildren will all need birth certificates and marriage certificates, if applicable ( all with apostilles and all translated)
You will also have to download several forms from the NY consulate's website that will need to be completed.
In the meantime, set up your appointments. During the wait time, you can begin to get your documents together.
It seems like a daunting task, but it's all quite doable and a lot of fun too. Best of luck.