The answer from CCP…
Greetings, GM Whiskers here,
Thank you for contacting EVE Online Player Experience Team!
According to section 3 of EVE Online - End User License Agreement, you are not permitted to transfer your Account to another person. If you wish to discontinue your Account please refer to section 6 of EULA.
You may transfer a character from your Account to another account, either belonging to you or another person. This transfer option is available from the EVE Online Account Management web site: https://secure.eveonline.com/
It is not prohibited to play with your family on alpha accounts together. Restrictions are applied to use of multiple Alpha accounts (or Alpha and Omega accounts) simultaneously by the same person.
Hope this will clear the situation for you. If you’ll have any further questions please let me know.
Best Regards,
GM Whiskers
CCP Player Experience | EVE Online | EVE Valkyrie