Third Wheel...What would you do in this situation?

I'd be honest with her about that. Just tell her that her birthday is important to you but you don't want to go on the train ride and be the third wheel. And no matter how much she's going to say, you won't, you will. And therefore you don't want to go. Tell her this should be a special time for just her and him anyway. If she keeps on about you going just tell her. I'm sorry, but I'm going like that. Then tell her he might wish she wouldn't keep asking because he might want it to be just then two as well. Then say I'll be there for your birthday but I got to go study as well. So go have fun and you can tell me all about your ride.