I am specifically prompted to insert my Google Authenticator code
That's right. Electrum would then send the code from Google Authenticator, along with your transaction, to Trusted Coin, who would also sign the transaction for you.
2FA can't be disabled unless you have the second seed which should have been given to you when you were creating your 2FA wallet which you claim you hadn't chosen.
That's not accurate. When you create a 2FA wallet with Electrum, you only generate a single seed. That seed is enough to recover you wallet entirely.
Do you mean I should create a new wallet within the application with seed original seed I have?
Create a new wallet, and name it something different to your current wallet. Select "Wallet with two-factor authentication", click next on the 2FA screen, select "I already have a seed", enter you seed, then choose to "Disable" your 2FA. Your wallet will be restored with 2 of the 3 private keys needed to sign transactions.