I really struggle with this too - self-compassion in general but especially when trying to apply it to past experiences/my child self.
I would say that for self-compassion in general, I just try to notice and accept and not judge/be critical. Still a lot easier said than done but I am getting better at stopping myself and trying to be more mindful of that about general day-to-day stuff/thoughts.
Re my younger self...whenever my therapist mentioned my younger self/my inner child I would have a really strong, aggressive resistance to it and would basically shut the conversation down (and if my therapist persisted, I would then dissociate) If I did ever get to speaking about "her" my words would be pretty punitive. A few months ago, we touched very quickly on the topic and my therapist said that my inner child doesn't feel safe with me. It was actually surprisingly hard and upsetting to hear that. I had gone from denying her existence/speaking harshly about her to suddenly feeling very sad that she didn't trust me. It was a strange experience.
Anyway - there is one recent example where something kind of clicked with me, so I thought I'd share it in case in resonates with you or maybe something you could try.
Before my recent surgery, I was feeling very anxious because there were two thoughts that just seemed to be playing on a loop all the time and it was very anxiety-making. The thoughts were:
1) my foot was going to be in traction for the surgery and I kept thinking that, with my foot in traction, i wouldn't be able to get away.
2) that I didn't want the doctor (or his instruments) inside my body.
I didn't flesh these thoughts out much more than this - there was just a building frenzy about my anxiety around these two points that just seemed to be on repeat in my head.
I could understand that these thoughts were probably as a result of stirring up memories from old doctor-related trauma. But I could also see that I was being stupid, irrational, obsessive, ridiculous, over-dramatic, that the anxieties didn't really make sense/weren't relevant now etc. Because not being able to get away because my foot was in traction was stupid and irrational - I would't be able to get away, not because my foot was in traction, but because I'd be unconscious! And I won't need to get away anyway. And not wanting him in my body was largely irrelevant as it was keyhole surgery, so I don't think he was actually going to be in there in any way anything. And not wanting his instruments in there...well...that was ridiculous because of course he has to put instruments in my body to do the surgery! Stupid!
When I told my therapist, she gave me a big explanation of the difference between here and now and the past and said that the feelings and the fears I was experiencing were real and correct but they were in the wrong place. So, my fears about not being able to get away and having things inside me were real and correct but that they belonged in the past, with other events and had nothing to do with the upcoming surgery. It was a really useful conversation and made lots of ptsd-related things really fall into place for me.
And then she said that calling myself stupid, irrational, ridiculous etc was probably the worst thing I can do - because the fears are not those things. They are real, correct, understandable fears based on things that had happened as a child. And that anxiety was now being triggered big-time by the upcoming surgery.
Then I asked, so how do I stop the thoughts because those two things are playing on a loop the whole time. And she said that when that "voice" starts to play (getting anxious around those two thoughts and then my "voice of reason" kicking in to tell me that I'm not making any sense, that I'm being irrational, so STOP IT!"), I need to try to bring it a different voice that will calm, reassure, support, understand, look after etc.
I had no idea what she was talking about.
So, then she modelled to me what I could say to my(younger)self and she spoke for quite a while saying things like "I know you're feeling scared because of what happened before, but that was a long time ago with someone else who did things he shouldn't have done. I know you're frightened and I will help you with that old stuff. But we need to wait until after this surgery. This surgery is going to be a good thing and I have given the doctor and all the medical staff there permission to engage with my body so that they can do the surgery and help to get rid of the pain I've had for years...." Etc etc. She said quite a lot and as I listened, I found it quite hypnotic. To start with I think I was listening thinking, this is weird, I can't do this. But then I found it incredibly soothing hearing her talking to "me" like that.
So...I went away pledging that I would engage with my younger self whenever the anxieties and the punitive language came up to try to reassure her and calm her down. And I did that every time it happened. And the anxieties began to quieten. And I still kept doing that every day in the run up to surgery, even if the two troubling thoughts didn't crop up. I figured I could do with all the calm and reassurance I could get so what was the harm?! :-)
I can't explain it and I am really surprised because it is the first time I have ever really been open to any of this younger self/inner child stuff. Maybe something just clicked? Maybe I was just so desperate to calm the anxiety that I was willing to try anything? I don't know. But it did seem to really help.
One thing I did notice was that, when I was introducing this other, more compassionate voice, it wasn't my voice. What I actually found myself doing was remembering what my therapist had said - so I was re-listening (in my head - I didn't say anything out loud) to her saying soothing things...it was her words, her voice or picturing her voice. The following week, I told her that I'd done this exercise every time the fears had cropped up and that it seemed to help but that I'd noticed that it was her voice/words not mine so I didn't think I'd done it right. She said it was still a very valid way of doing it - that even though I had not felt able to use my own words and voice, I had still chosen to "press play" on her compassionate message rather than the usual one I would have played and listened to, telling myself I was being irrational, ridiculous and obsessive etc.
I am still not in any way totally down with this stuff - far from it! But I was very surprised by how effective this exercise was. It really, really helped. But without my therapist modelling it to me and me then using that when I was on my own, I think I'd have been totally lost and wouldn't have known what to do. And then I probably wouldn't have kept trying. Could you maybe ask your therapist to do something similar - she give you a demo of how you could speak to yourself differently with an example that comes up for you? I actually really wish I'd have recorded her...it was a surprisingly soothing, moving experience listening to her, whereas I would have expected it to just feel really cheesy and fluffy and yuck!
Sorry this is so long, but I wanted to say 1) I understand the challenges of self-compassion and 2) That it is possible to make some headway.
Good luck!