It sounds to me like she may have been hand-raised but poorly socialized maybe. And let's remember all of them are going to be different, just like people. You might have gotten an introvert. My little Jewel has only been with us around a month, but she was heavily socialized by the owner of the pet shop. The owner had her employees handle the parrotlets many times throughout the day and let customers hold them whenever possible. It was in fact why we bought her, we fell in love in minutes.
But she was a bloodthirsty little thing. Not aggressive or fearful at all, just... wanted to bite and see what blood tasted like I guess. I almost got a pierced ear and nose and still have a little red spot on the web of my fingers.
But with patience and work she has learned not to actually bite to hurt. She knows what is appropriate and what isn't and when. I can tell now that some of her nips are a way for her to ask for some petting and grooming and cuddling. She will peck me gently until I start scritching her, then she cuddles up in the cupped palms of my hands in a way I have never seen another bird tolerate, like a cat she wants to be cuddled and stroked and warm. Most birds hate when you hold them with a closed hand...
So I guess in a lot of ways I am lucky and it's just my bird's personality. But here are some tips I learned from other birds (some are just echos of what others said already).
PATIENCE: These birds live up to 20+ years. If you do your part, they will bond or at least warm up to you.
BONDING: Time and positive reinforcement equal bonding. But do not force the interaction. Encourage and allow it. Make sure they know they can leave the encounter.
SPACE: They need a space they can call their own. Parrotlets are highly territorial, even with their own mates and kind. Mine loves to be on me, with me, etc, but part of that is because I leave her in her cage and do not pester her a lot till it's playtime. I do not lurk standing at or over her cage talking to her staring at her. Instead, I keep her cage "near" my own area of work. About 5-10 feet away, so I'm always visible and frequently respond to her chirps with little chirps and words of my own. I do NOT go into her cage except for maintenance and related duties. When she comes out, I open the door and either back up and let her come out, or stay close enough for her to come to me, but I do not put my hand in the cage or even touch it or go near her till she clears the cage doors. If I can help it, I want her angling to fly to me before I reach out and help her step up.
TRAINING: Target and clicker training are great according to a lot of people. Sadly, I lack the patience to use them religiously, but I use mouth clicks and words, and hand gestures instead. She knows what little smoochy sounds mean now, and little clicks, and good girls, and she knows when I tap my finger on my shoulder I want her to go there. Since she isn't super tame with you, don't use scritch rewards, use food rewards.
TIMING: Parotlets need tons of playtime, but structure and timing is just as important. Are you only taking her out at bed time when she is tired and cranky from being alone all day? Does she get a good 12 hours of sleep with pretty strict bedtimes? All of these can make a nice bird mean and skeptical of their owners. We wake up Jewel around 7 AM, and put her to bed no later than 8 unless some special circumstance happens. So she always gets between 11 and 13 hours of dark time in her cage to sleep. When we work outside the home 4 days a week, we might keep her up an extra hour or two tops, but we only take her out for maybe an hour at most. And the moment she gets aggressive or anything she goes in the cage and lights out. On days when I am home, I have a daily routine, I give her a piece of broccoli while I do my morning chores, and she eats that and watches me. Then I eat lunch, when I am done, I take her out for a while. usually about a half-hour to an hour. It depends on how she is behaving because I have other stuff to do, and a naughty brat gets in the way. Then around 4 or 5 I take her out again for a while till I have to make dinner. so figure about an hour. Once she calms down a bit and is able to be a little more well-behaved on my shoulder or entertain herself around the room, I will let her out a lot more. But the timing and schedule is important.
TERRITORIALITY AND NEUTRAL SPACE: More than simply respecting their cage space, sometimes they are nervous because they feel forced into your space. Consider going into a neutral room or part of the room. One set aside for interaction. One that is just unfamiliar enough to cause her to depend on you for stability and normalcy, and this new space becomes your shared space, and bonding may be easier. If you are always on the couch or on a chair, and your bird knows that, they might think that is your space and feel like an invader, and this could make them feel uncomfortable, or make them aggressive.
CHEMISTRY AND SELECTION: Let's just face it, some birds and some people don't mix no matter what you try to do. Despite being a 6'1" 245lb strong guy with a mohawk, animals usually love me. I rarely meet an animal I can't bond with. But my wife often struggles with the same animals I bond with. So why is it? No idea. My wife loves animals too so it's not like they sense her dislike or something. I don't believe in forcing animals to bond with people, but usually, they do, so I wouldn't lose hope. Just be patient and be worthy of that trust. Tell yourself internally that your bond isn't just because you OWN her but respect her little soul as important and she should choose you too. And when she does choose you, lavish her with affection and food. Even just that little mental/spiritual shift can be felt by animals and they respond to it very well.
LEARN THE LANGUAGE: you probably already know parrotlet body language and chirps and squawks. And while not all birds are the same, some things carry over between all of them as part of their instinct. Tail splaying is a common sign of alarm and aggression for them. It's how they signal to other birds they are scared or distressed. Of course, sometimes they can do this for other reasons (pooping and just plain old stretching comes to mind). But if coupled with other signs it's a sure thing. Hackles up - If you see the area behind her head puffs up in a weird way that is often a sign of aggression and fear. Added to tail flaying you are in for it. Rapid peeping and charging - Jewel likes to charge things she doesn't like and peep like she is telling it to F off. Head out on a long neck and looking around a lot - Concerned, excited, maybe looking for a flight plan to escape or investigate, not likely to bite, but likely to fly. try to move and act calmly. Hissing, mouth open, sometimes this is play, but if coupled with other signs, it's fear and aggression, watch out. if so do things to calm them. Head down wings out, body puffed. this is a maximum threat. Back off now!
BACKING OFF: Never and I mean NEVER react. Instead, Act. It's tough to explain the difference, but never flinch when they hiss, bite, or otherwise do something aggressive. Slowly change what you are doing or distract them. The only time you make sudden moves or show any kind of pain is if it's causing real damage. Parrotlets are evil incarnate, and if they think you are in pain because you yelped and pulled away, it becomes a game and they will tease you. They only care about hurting you if they really go over the line and only when they care about you.
DO NOT CROWD OR FLOOD: Do not force birb to do anything, do not grasp them, or shove stuff in their face till they do what you want. offer at a safe distance, and use patience and repeat encounters instead. I have had birds who didn't mind something at first, get flooded because I thought they were ok with something, only to have them learn to hate that thing because I rushed them afterward, and now It's an uphill battle to get them to tolerate the thing anymore (harness training in this case).
YOUR OWN LANGUAGE: you don't have feathers, wings or other things they understand. So you have to keep it simple and vocal and use treats and rewards. I like using chirps and kissy noises and clicks and soothing words with the occasional No, or hiss, or irritated squawk.
There is probably more I could say - but I forget. And also Since you had a baby for so long you probably knew a lot of this already. So don't see this as any kind of insult, I just have a problem with being over precise and complete. being a little Neurodivergent does that LOL
Let us know how it goes!