Welcome to FT!

treblig, I can't tell if you are actually travelling with your wife/kids or if wife/kids are travelling on their own without you. It sounds like the Amex is in your name.

So to be clear:
- If you is travelling on the same reservation as wife/kids; the Amex benefits of Zone 1 boarding and free checked bag will extend to wife/kids also.
- If you is NOT travelling; wife/kids will not receive early boarding or free checked bags.
- Wife/kids should each have their own DL SkyMiles account/number, and that number should be applied to their tickets for this trip. Since they are starting from scratch, the only benefit this will really give them is the ability to earn miles, but it doesn't cost anything and the miles don't expire so there's really no reason not to have an account. Miles only credit to the account of the person(s) flying, so if anyone doesn't have their own account, nobody gets the miles.