Wow, what a conundrum. This issue sounds like it's one that's really affected you. I wonder how you came to believe you have a poor attachment, and whether you have ruled out other issues such as ASD or other diagnoses that may explain or help you to better understand your child's needs. I know it's early days, but perhaps a diagnosis might be useful down the track.
I'm going to move right past the Alpha Child label and come back to that, I'm going to start by explaining attachment.
Based on her work with a specialised experiment where children were left without their mothers in a room with a stranger, Ainsworth (1970) posited there were three main attachment styles. The first was secure attachment. The second was insecure and avoidant - a resistant attachment style. The third was insecure and ambivalent/resistant and was termed avoidant.
Secure attachment was seen in the child being distressed when the mother left, in being wary of the stranger when alone but comfortable when the mother was there, being happy when the mother returned and using the mother as a safe place from which to explore the room. The insecure/avoidant attachment style was termed resistant because it was seen in behaviours such as being intensely distressed when the mother left, avoiding and showing fear of the stranger and, while approaching the mother on her return, pushing her away or avoiding her when she was comfortably in the room. This style also saw the child not being curious when the mother was there; the children exploring less of the room/toys and tending to cry more than those children with other attachment styles. The third style, avoidant, saw limited or no signs of distress when the mother left, was comfortable with the stranger and mother’s presence and neither presence seemed to affect them much. Children with this style also showed limited interest in the mother returning and both mother and stranger were equally able to comfort the child when it was distressed.
This work mattered because, Ainsworth suggested, securely attached infants were easily soothed when upset. I wonder if this not being able to be soothed is an area in which you are seeing issues? It's not unusual for a three-year-old to be inconsolable about stuff that is, to us, probably a bit silly. They are often referred to as 'threenagers' because of, well, their capacity to throw an adolescent tantrum without the hormones, the grunting or the need for Lynx Africa.
The insecure/avoidant styles of attachment rejected their attachment figure. They were either not clingy enough or rejecting of the attachment figure (insecure/avoidant) or too clingy (insecure/ambivalent) but both styles were a rejection of the attachment figure. Do you see that with your child?
It's never too late, particularly not at three, to work on enhancing the attachment style. Doing things you both enjoy, together, and with love are a great way to improve the relationship.
It's also important to learn to say no with kindness, gentleness, empathy and respect for the child. I haven't seen any examples of why you think your child is an 'alpha' child, but perhaps you need to set firm limits, hold those limits where appropriate and avoid punishments (and rewards). This might help give you both the relationship reset it seems from your question you're asking for.
Remember to say no without judgement, to hold the limit where it is necessary and to empathise with your child's feelings of being told no. We all hate it when we get a no, but, what we want from those who love us, is for them to listen, to empathise and to respect our feelings. They can't change that no, but they can be kind and listen.
That might help you with your issue.