I think there is a lot to be said for handling this process with honesty, transparency, and integrity. These are core values for any solicitor, and it is worth starting to practice them now.
Personally, I would disclose to the firm that offered the TC that before entering into the contract, I intend to complete the vacation schemes I have already committed to. This shows you are looking to make a properly informed decision about your career. I would also let the vac scheme firms know about the unsigned offer to see if they view it as a conflict. Ultimately, seeing how each firm reacts is a great way to gauge their culture and figure out if you actually fit there.
I don't particularly agree - I had conflicting VS last year, where one had a TC option and the other did not. I chose the one without the TC, and the other PFOed me from their TC app with what seemed like extra zeal.
Ultimately there are plenty of other quality candidates and it's risky to be too open about what you're up to.