You could periodically create encrypted backups of the necessary data on a USB stick (stored in a known place in your home), so that the data locker only needs to disclose a relatively short password to her (and it could even broadcast it in a tweet, since she would be the only person for whom that password would be useful).
Then, as you say, if she wants to access the plaintext, she would have to click a button on a secret web page somewhere which would trigger a server to send an email to you (and a couple of friends) saying that she had done this and that a 24 hour timer had started.
The email would also include a link to a page that could reset the timer, up to N times, while you tried to buy a new phone or regain consciousness or post bail or whatever the attack scenario is that you want to defend against.
In practice, the most likely failure mode is that you don't need to use this system for years and then something silently breaks, like you forget to renew a domain, or you forget that you changed your email address. As such you should include a quarterly test process for all of the steps, including making sure your partner remembers the process for performing the decryption, and making sure your friends haven't marked the automated email as junk, and so on.