I wouldn't be happy about it either.
The worst part of any infidelity (that might sound like a strong word to use here, but bear with me) is the emotional attachment your partner has to somebody else. Sexual infidelity is bad enough, but emotional infidelity hurts much, much more. You're right: it does sound like she has some unfinished business going on there - possibly wrapped up in some guilt she might feel for not supporting her ex in transitioning.
This line in particular stands out for me:
Quote from: Darrin Scott on November 18, 2013, 07:46:11 AM
They didn't talk for a year because her ex wasn't being respectful of our relationship.
So her ex has disregarded your relationship before, and now your fiancee appears to be playing along to a certain extent. Her behaviour seems disloyal and it's getting in the way of your ability to trust her... and as we all know, trust is essential in any intimate relationship.
Writing to her is probably a good idea, but perhaps not whilst she's at work because she'll react in some way and she probably wouldn't want that to happen in front of her colleagues. Talking face-to-face runs the risk of getting too emotional, but that risk is reduced if you go out for a meal together.
I think you're perfectly justified in telling her how much you love her and how much she means to you, and whilst you're more than willing to help support her ex you need her reassurance that she's there for you first & foremost. You're perfectly entitled to say that you're not comfortable with her getting too attached to a person who has been disrespectful of your relationship in the past.