I got this from the official rules page:
Except as otherwise set forth in these Official Rules, prizes won by a person who is a minor in his or her state, territory, province or country of residence ("Minor") may, in Sponsor's sole discretion, be awarded to his or her parent or legal guardian, and, in the case of prizes that, in Sponsor's sole discretion, require winner verification, that parent or legal guardian will be responsible for completing the verification process and executing all "Prize Claim Documents" (as hereinafter defined) and otherwise complying with all requirements imposed on winners set forth herein. Notwithstanding the foregoing, and unless otherwise permitted by Sponsor in its sole discretion, in the event a Minor is the winner of any prize in which the winner is permitted to travel to, stay at or attend an event, site or destination, such Minor and any guest (as applicable) must be accompanied by his/her parent or legal guardian on such prize and, as applicable, the parent or legal guardian will be considered one (1) of the allotted guests.
Therefore, yes, you can send in for your kids.