Try and depersonalise it a bit. If this was a close friend of yours, would you say they should feel shame?
No - I read stories here of people trying again and I don't ever think that they should be ashamed of their behaviour so I guess I am being hard on myself here.
We all wish we had been braver/stronger/wiser. But we're not born into this world with an instruction manual. You did what you thought was best, I am presuming to keep things together, to allow him to hurt you in order that you stayed together, kept the family unit as a whole. It may not have been the most healthy way, but you tried, the only way you knew how. If we could all be perfect, life would be so much easier - but we're not. And you tried.
I said again and again that I did not want to reconcile for 'the sake of the kids' - that we had to both want to be together. But it was so good to be a family for the times he could manage that (we had been a family for a long time before the first split). He was seeing a T and so I felt each time that it was worth trying again - there was always that increment of a difference in the right direction to help me rationalise an ultimately unhealthy choice! I am much less of a perfectionist than I used to be because I realised that trying so hard to be in control of everything was disastrous. However, I'm not totally cured! I tried really hard to be perfect and in control and then I tried really hard to let things go and not be perfect and now I'm not entirely sure what to try. But maybe I won't try so hard

You're also not responsible for your FOO's hurt. Many families stay in touch with a spouse who has divorced their loved one - that's between them and the spouse. It's not your fault that he has cut them off. He is an adult and made his own choices.
I do find this hard. My family isn't perfect (but no worse than most) and I could share my frustrations with my exH but now I feel guilty because I think he has used this to justify his blackening of them. They really struggle with the lack of closure in the same way I do.
There's nothing you can do about the past except learn from it.
I let plenty of people down in my life but I've taken steps to improve it and that is all I can do.
I made a bad mistake just at the point that the initial crisis occurred. I 'ran away' from the shock and fear (this was before I knew about BPD) by becoming infatuated with someone else for a while. I did learn from that - in all the times exH and I were separated, I did not date. I wanted to make sure that I was healthy in case I dragged someone else into a mess. i started to see a T and I am proud of the way I have grown over the years despite the drama and chaos and heartbreak. fakename - your post has reminded me of how far I have actually come. I need to concentrate on that instead of wallowing in shame.
Did you speak with your children about it? Perhaps there is a moment when you can tell them that you feel really sorry being not so available for them in the past? Or something like: Next holidays we will do ... . together!
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Yes - I have apologised to my children for not being as emotionally available at times as the probably needed. I have tried very hard to maintain some stability for them (no more moving house) and regular treats or time together one-to-one rather than huge gestures.
Thanks guys for the responses - feeling a little more grounded today.