In sending the first-signed transaction to another for second signature, how does the first signer authenticate to the second without compromising the independence of the two factors?

Not sure what you mean. The idea is the second factor displays the transaction and the user confirms it matches what they input to the first factor. Ideally, using BIP70, but I don't know if BA actually uses that currently.

It's the same model as the TREZOR, except with a desktop app instead of myTREZOR and a phone instead of a dedicated hardware device.