>>42502642 (OP)
Her hat and cape are physical representations of her ego almost. It's a subtle writing choice, if she does this (ignoring perverse implications on these threads) it means she's so happy she's willing to temporarily be vulnerable.
My headcanon is, not only is that stallion look-alike her father, he also only pretended to love her through foalhood but shamed and kicked her out of the home for messing up a magic act he'd had her perform in. High parental pressure and things like that, not too original ik. Maybe her relation with her mother could be explored too, perhaps the father was abusive and damaged her mentally where she had to be institutionalized, as he's all about the money and will even cut ties with their daughter over it. Mother protests this move, he loses it. Trixie loses the one source of genuine unconditional support her mother gave her.
This is when she shortens her name to Trixie and travels in her wagon, to reclaim the part of her self-worth that got crushed on stage. Going to any lengths, even using an alicorn amulet, to further herself.
Starlight may have briefly cracked the shell she'd built around herself, but Twilight came in at the worst possible time, bitching about silverware etiquette, and Trixie unintentionally put her hoof in her mouth. Besides a brief shallow apology at the end of the episode, Twilight has done nothing to take ownership of her actions and how they affected someone without a Princess title. Which is why, while I don't hate Twilight, I've always gotten an uneasy feeling about her when she's around this pony.