It doesn't appear that it violates the rules if another person in the household enters from the same computer, but they have to have their own assigned email account. I think your best bet is to use regular ISP email accounts on these and not "free" email accounts. I know that some sweepstakes don't accept entries from some of them, because the free emails are what people use to get multiple entries. If they have to pay for each email account, they probably couldn't afford to cheat. This is what eprize has for that part of their rules:
Each participant may enter one (1) time per day, regardless of method of entry, during the Promotion Period. Multiple entrants are not permitted to share the same email address. Any attempt by any entrant to obtain more than one (1) entry per day by using multiple/different email addresses, physical addresses, identities, registrations and logins, or any other methods will void that entrant's entries and that entrant may be disqualified. Use of any automated system to participate is prohibited and will result in disqualification. In the event of a dispute as to any registration, the authorized account holder of the email address used to register will be deemed to be the registrant or player. The authorized account holder is the natural person assigned an email address by an Internet access provider, online service provider or other organization responsible for assigning email addresses for the domain associated with the submitted address. The potential winner may be required to show proof of being the authorized account holder.