You just sign up for the e-mails and they will e-mail you when the super family rate comes out. Then you have to phone them right away to get the rates. I got an e-mail in July and they had the dates that we already booked for our late August trip, so I called about 1hr after the e-mail was sent out and waited on hold for about 10 minutes. 2 of our 3 nights were still available under the promotion, so they applied the discount to the two nights on my reservation that I had already. Then I had to bring a copy of the e-mail to show at check in. The rate isn't good for suites, though.
They also have an AP rate of 20% off and you can use the online code LNAP or there's the Disboards discount that anyone can use for 15% off using the code LNDB. You can't combine these with the super family rate, though.