Find an interested, serious and motivated person in Your site member list from Your family, talk with him/her, and promote him/her as a site manager.
By the way, it's always a good thing, to have a 'site manager deputy'. The site managers should talk together and adjust activities on the family site.
If You feel, it's time to go one step back, You can send an email to the support at email@example.com with the request to change the site owner to the high motivated 'site manager deputy'. So, after this change, You are 'just' a site manager with a lot of experience. If the site owner deceased before, then the 'site manager deputy' must send the email with the site owner change request to the support.
These are the steps I will do for our family site.