I’m sure your whole family is more than welcome to signup if they want to.
Like Scott has suggested, I too think the TOS appears the way it does in order to keep the evil promocode players/ultra-heavy users at bay. Dreamhost appear quite happy to make 1 on 1 arrangements regarding accounts and it would of course be in your best interests to contact support to tell them your dad, sister, etc. would like to signup for an account just in case they think you might be trying to cheat them on the awesome signup bargains.
Maximum Cash Discount on any plan with MAXCASH