Hi,
Thank you for sharing your question. I get how frustrating it is when a family member can't get into their Hotmail, mostly after a security alert and a bunch of failed tries to get it back.
What normally happens is that the account recovery info is old, and the system can't prove who owns it. To fix this, it's best to use the Microsoft Account Recovery Form at https://account.live.com/acsr. Give them as much right info as you can, like old passwords, what some of the last emails were about, and anything else hooked up to the account. If getting it back doesn't work, you can reach out to Microsoft Support at https://support.microsoft.com. Just click Contact Us and pick Microsoft Account & Billing to chat or get a call from someone.
I hope this helps.
Best Regards,
Noel