Changing core issue is the hole point of having a therapy. It is not that easy.
I can give you an example. I used to have this feeling I am not lovable. Just a huge body felt. Like I know I have brown eyes. I had this feeling. So I carry it around me for a long time. Whenever a relationship ended, no problem. just proved one more time, yap! I am not lovable.
I was not in therapy at this time but I read some books about CBT and I went really down asking myself why I felt that? I keep asking the question until the answer broke me down - the truth hurts. I do the same for all my therapy related feelings now...why do I hate him? why am I anxious around him? why do I want to correct him? you get the rift.
As I realized, I was not loved as a baby by my mother and cried like a baby for my loss. I came to realize that I have to accept I am not loveable (remember this is self help) so I accept it what I found. But I made a little twist, now I promised I will love others. I will take a risk of loving a person even though I am not loveable because I was never loved and it was true what they say that whatever happened to you as a child will stay the same as an adult (again this is my screwed up brain trying to heal itself). I was not loved but I loved my mother is how I rationalize it.
So I healed by accepting this core issue - not being loveable -and focused on be loving to others. My life changed in significant way and eventually I re-worked on this issue and realized, I am both loveable and able to love and it is not sum-zero game. but that took a life time.
Core issues heal much more integrative and holistic way when you have a good therapist that you and him/her can re-enact the time where you got injured/hurt and re-work it through provided you recognize that is exactly what you are doing and can verbalize the process and the result being sought after.
A good example is when one has strong loving feelings toward a therapist, that is a core issue that is looking for reintegration or when a therapist is late or goes away and the clients go nuts, all these are core issues coming to the surface looking for attention from the clients for reworking. Most core issues are healed in the process of a relationship..fully and holistically and faster. What happens that I notice is a lot of therapist will not actually say this is your core issue, they may go around it for you to name it. That can take a long time. Then you name it and now what? Then now the therapist cancels the last minute session and you are fuming, and the therapist just keep asking you tell me more about your feelings and on and on. But the core issue is abandonment or the ballpark (attachment etc). And if you are really motivated, you may recognize this because you did not do the same when a friend cancel on you last week. So you may say what right do I have to be so angry at the therapist? then you can tell the therapist you were pissed off for the cancellation and the feeling was a bit too strong for an adult you...and must be a core issue...and boom now the therapist is perked up to help you resolve this because you bring it to the door. aot of people will choose to focus on the anger at the therapist and will not make that loop to the core issue and that my friend is why you may stay in therapy and look for the core issue forever. You know it but not looping it. You stay with it at the therapist and never connected to teh past and keep going until it means nothing in your gut!
Since you have therapy, it is probably better you allow that vulnerability to witness yourself in re-enacting of the core issue trauma moment (in feelings usually not in real memory all the time) and go through it to come out the other side and feel the triumph of living to tell it.