If a user ( in this I am using this procedure ) open calendar application , right click on home if I click on gmail address ( this is same same web mail address / gmail address of a person in my family ) , And also Apple ID is kept same as gmail address and in system preferences > iCloud the user is signed with Apple ID .
The calendar will be shared because the person is in my home or work place under the same network connection and the data is saved in contacts ie. address book ( including his gmail address and other credentials ) .
And if I click on iCloud address it will not share because my server is stopping to share .
The same procedure applies to the person in my home who try to share the calendar with me .
Same method applies to you and your brother .
And if you are not using gmail account then ? create a gmail account , as iCloud calendar is just an configuration with web mail services ( could be gmail , yahoo or any ) .
To work properly , both user must be signed in with the same procedure and obviously it totally depends upon your internet service provider .