Sure, go ahead. It would help give me some ideas on what to do.
So, to start off, Missy's canon trigger event was caused by the utter mess that her parent's relationship was, with one especially bad fight serving as the straw that broke the camel's back. There is no need to change the broader context in my opinion.
Laetitia!Missy is a Missy that tried so very hard to improve things between her parents. She put so much effort in, in fact, that nearly all other aspects of her life suffered for it, such as her schooling and social life. But, through a combination of sweet-talking, throwing scenes whenever her parents were about to argue, guilt-tripping them and many other tricks she did actually manage to attain her goal. For once, her parents were... not affectionate with each other, but things are not bad either. They stay like this for days, maybe even a whole week, leaving her to bask in an afterglow of vindication. And then, everything returns back to normal, all of her invested effort and personal sacrifices chewed up and spat back out into her face. But, at this point, she very well may be the person most invested in making the relationship between her parents work, so she isn't giving up.
It's at this point she triggers with an ability that outwardly makes her a tinker, but is more complicated under the surface. She crafts a special, tailor-made gift for the intended recipient, which may, at most, give some weak beneficial effects to their owners. These gifts, however, do not actually spawn the spider friends - they only serve as a way for the shard to mark who is going to get chestbursted. As a consequence, Missy would have a low-level awareness of her giftees, receiving rough knowledge of their position in relevance to her - though not precise data, more of a colder-hotter deal - and if they broke her friendship. The conditions of that are also dependent on the emotional and social relationship she had with the giftee prior, the specifics forming outside her control. As a side note, there are some parahumans who seemingly don't age or do so very slowly past their trigger in canon, so if you want to preserve the Laetitia aesthetic, you can just tack this on.
Personality-wise, she no longer believes in the honesty or reliability of emotional bonds. She needs to have a gun pressed to someone's head to think of it as sincere and, much more importantly, safe. As I said, she also feels bitter regarding the wasted sacrifices in her personal life and would seek to reestablish it, speeding things along by abusing her power. This Missy is
very likely to quickly rack up a body count, if only by killing her parents.
Happy Teddy Bear!Missy, on the other hand, gave up on the relationship between her parents but not on her relationship with them. Ultimately, she ended up hanging on by a very toxic thread; her parents use her as a tool for hurting each other or showing each other up, and while she may hate it, it is still attention and better than abandonment. She may even play along when she feels particularly threatened in this way. One day, however, they simply get tired of it, treating her as an afterthought. She tries, again and again, to get their attention back, but they get fed up with her attempts and all but throw her into her room to get some peace and quiet. Alone and despondent, she takes in all the toys she accrued over the years that she never spared a second glance, her eyes settling on a teddy bear left to gather dust on the corner of a shelf.
Her trigger gives her the ability to transform her arms into large bear arms instead, just a little plushy in appearance. They are both stronger and more durable by several magnitudes over the human ones, easily withstanding gunfire and breaking steel apart. Thing is, whenever she feels particularly anxious or afraid, the transformation may happen involuntarily. Additional bear traits are optional.
The part of her that suffers most, in this case, is her sense of identity. She adapts her personality and behaviour to whatever she feels will get her the attention and approval of others, always nervous under the surface that it's not enough and she'll be abandoned again. For example, if she were to become a ward, she will be perfectly happy playing the mascot, as long as her superiors, at the very least, show their approval and give her a solitary, patronizing pat on the head.
Bloodbath!Missy found nothing to hang onto, simply sinking further and further into the misery that her life was becoming. Emotions piled up over time as her environment wore her down, and no way of expressing, let alone processing them was available to her. Randomly, she overheard some of her classmates talking about self-harm - specifically, cutting one's wrists. The context itself doesn't matter to her, simply that the idea wormed its way into her head and won't leave her alone. The temptation grows too much one day, and she hurts herself a little, just a paper cut, really, and feels almost liberated. It's wrong, she knows it, knows what it can lead to, but for the first time in a long while she has a way to relieve what she's feeling. Things don't get the chance to escalate to that point, however, as her parents catch her hurting herself again at some point. The situation is ugly and stressful, they are screaming at her, none of their worry actually meant for her but for their image, their screaming quickly becoming directed at each other as they start blaming the other party, her feelings dismissed in favour of their bullshit once again.
Her power here can be divided into three parts: hemokinesis, negative emotion amplification and blood production. She can control several bathtubs' worth of her blood with excellent precision and decent range, capable of sharpening the fluid to cut into human flesh, though too weak to break through terrain. Anyone covered in her blood, no matter how little, will feel ennui creep into their being, their mind and emotions becoming darker and darker as coverage increases. The effects, if the blood is washed off in the next few minutes, will not be permanent and, even if they do become such, the potency is lowered considerably. However, if she manages to fully submerge somebody for a while, they very well may become suicidal. Her power also produces and replenishes her blood as she uses it, ensuring she doesn't die or is affected by blood loss or infection. A mild resistance towards emotion-altering effects may be present.
Ultimately, Bloodbath!Missy is someone who is both bitter and lost, yet wants to stand the ground of their misery, believing it to be one of the few things that will stay with them and is true for them. If emotional effect resistance is present, it is likely her shard is affecting her behaviour, making all of this go double.