Sazzi forget the blame game. What has happened has happened and what you need now is advice on how to put it right.
It will first probably need sometime sorting the problem out. Write down exactly when and why the accounts were opened and their purpose and then track down the exact dates that the bank -messed it up- made their mistake, attach a copy of the two statements showing this to the narrative you are writing. then continue the narrative , with everything else that happened -other childs account closed down etc etc. Attach a copy of the relevant bank statement to your narrative at any time.
Then sit down read it through double checking everything you said, so that you have a narrative that can act as a constant reminder to you of exactly what happened.
Next write a letter to the bank briefly stating what happened and what you want - the whole thing sorted out to back as it was meant to be, then attach a copy of your narrative to the back of the letter and send it to the Chairman of the relevant bank. It is possible to get his name and address by googling 'Chairman YY bank address'. Do not bother with the local branch they will just try to see your off.
If that does not work, or even beforhand,make an appointement with your Citizens Advice office, they have skilled financial advisors who can help you as well.
Whatever you do, make sure you keep the original ofthe narrative and the bank statements. Send every communication by recorded delivery.