Yes it does make sense.
Having been beaten and abused by a parent does not just inflict physical injury, but mental injury too, and that is a serious and longs lasting hurt that takes time and most probably professional help to reduce down. After all it is the very person you instinctively look to as a child for love and protection was the source of the prblem.
You coped by trying to avoid beatings by working to the most unreasonable of expectations - entirely natural though now no longer necessary at all except possibly inside yourself. A coping mechanism to be un-learned.
So yes you are injured, but no, there is no way you are broken, if you were you would not recognize what is happening and not have any will to sort it out. You see the problem, are seeking better, and getting assistance.
You are injured, yes, broken no.
Look at what you have achieved, not only in terms of success -though that does reflect your inbuilt abilities, but in having a family for 25 or more years, with a partner and children and you use words like amazing and marvelous. This is a wonderful thing to have done, particularly as I'd imagine trust in others might have been hard to find.
These are not the actions and accomplishments of a broken man, far from it
My own experiences with my parents, while I was with them, definitely made trust harder.
Now, holding all this together without family support and only a psych is a very difficult path. Do you think it might be possible to confide in a family member -your amazing wife for instance - so you have someone to talk with when down ? It made a huge difference to me.
They do not have to understand what is in your head -mine did not really -just listen and show they care, that's all.
Incidentally if you do find that magic switch that cures all in a flash, please let me know:) I don't think even the Amazing Mumfort's magic wand can do that. As Sophie says it takes time, but then again most injuries do.
I hope you feel like coming back and talking some more