First of all, your violations of their strictly enforced Terms of Service caused them to disable your previous account (i.e. inappropriate content, harassing/threatening other users, false accounts, possessing multiple accounts, etc.).
Second, your new account was deleted after the original one was banned. The aforementioned rules clearly state it you can't create another new account after it was disabled. They recognized the pictures, personal details, and email address on the new one and auto-banned it outright.
Third, your family members are also being banned is because of their use of the shared internet connection. Facebook carefully watches the IP address of them opening new accounts and also banned them on the spot.
Of course you should be mad, but remember you brought the whole thing onto yourself by violating the Terms of Service that resulted in your original Facebook account suspended.