Ooooh, quoting. Let me quote your quote!
Do you have a copy of these laws that shows that Miss Militia is in violation of them by not arresting Vicky on the spot? Or that arresting Vicky on the spot would be supported by them? Because none of those laws exist in our world, so unless someone published a list of them we don't know what they cover.
Given that what Vicky did was attempted second-degree murder
by a parahuman against a member of the Wards, who are
government-sponsored superheroes working
in conjunction with a law enforcement body, it's certainly well within the PRT's jurisdiction to have her arrested. That is, parahuman victim, parahuman perpetrator.
The 'special set of laws laid out for capes', in context, would seem to be laws defining how Protectorate capes can act within the law, upholding the law, while still maintaining their secret identities and using their powers for good.
I'm not going to claim specific knowledge of the laws because Wildbow didn't post them anywhere, but unless you're willing to try to define how they
don't parallel our laws for the most part (especially the part about arresting suspects for violent crimes) I'm going to assume they do.
You see, when you make a change to any setting as part of a fanfic, you have to be ready to deal with the knock-on effects. Canonically, PRT, Protectorate and Wards all arrested people. The assumption in the story is that they had normal arrest powers and that they arrested people for the same general things that cops arrest people for these days. Their right to arrest anyone wasn't addressed in-story because they just did it and readers accepted it.
Now, this is your story. I'm not saying any different. But if you're going to bend the setting to defend the odd behaviour of your characters, that's fine. However, it's then a good idea to keep in mind that this presupposes a wider effect. If Protectorate and/or Wards are not allowed to arrest people without PRT being there, that muzzles them considerably. (Also, I can't see Rebecca Costa-Brown setting up a system where Alexandria can't arrest people).
Likewise, there's nothing stating that Miss Militia
has to arrest anyone. Except that she's shown to be a stickler for the rules, all the way through canon. And when she comes to the door, she has
no idea why Vicky did what she did. It's not a hard mistake to make, writing actions for a character that are informed by knowledge that you, as the writer, have. She walked up to the house in ignorance of what was happening. What if Vicky had been Mastered? You knew she wasn't, so you didn't have Miss Militia think that, but it's entirely possible, and it would fit the situation. MM's calm approach would've been utterly wrong. Bottom line? Miss Militia was incredibly lucky, and somewhat reckless, in the way she approached the situation.
Overall? I've been enjoying the story so far. This last chapter, as you know, sat wrong with me. I've explained my reasons, in depth (to understate matters considerably). I've offered suggestions on how to fix it (without having Vicky arrested, even). Might I just say that accepting constructive criticism is actually not a bad habit to pick up?
Over to you.