Sending, receiving, and organizing email in Outlook.com
With Microsoft 365 Family and a personal Outlook.com mailbox, there isn’t a supported way to give two family members shared/delegate access so all three of you can read the same inbox and send/reply from that address independently.
Microsoft’s mailbox-sharing and delegate features require a work or school account using Microsoft 365/Exchange Online, basically it is a Microsoft365 business tier license.