Well, I've signed the money over to her, and I signed it with my key. Now if she signs it and broadcasts it, 2-of-2 multisig is unlocked.
You didn't create a signed transaction and sent to her.
The whole process starts with the recipient (Bob) creating a secret
R and sharing its hash with the sender (you).
Then, based on this you are going to create a HTLC with a timelock. This basically says
'I (you) pay X btc to Alice if she finds the secret R during the next Y blocks. If not, the funds return to me'.
Afterwards Alice (using the same hash) creates a HTLC with Bob where she pays Bob X (- fee) btc. The HTLC basically says
'I (Alice) pay X btc to Bob if he finds the secret R during the next Y-1 blocks. If not, the funds return to me'.
Now Bob is able to retrieve the X BTC using the secret
R. And as soon as he does, the secret will become available to Alice as well.
Now the only concern is that if Alice-Bob channel expires earlier than Bob-Charlie's, Charlie can maliciously withhold the preimage until A-B channel expires (and Bob can't take Alice's funds, because he can't provide the correct preimage to form the unlocking script, and Alice takes them all because the timelock expired), while Charlie publishes the preimage in time after that to grab Bob's payment;
You might want to read this:
https://softblocks.co/lightning-network-in-depth-part-2-htlc-and-payment-routing/The 'Broken channel'- and 'Rerouting'-part should clear your concerns.