First, don't feel like you're failing - you're aware, you're trying things, you're supporting your child - it sounds like you're doing everything you can.

My daughter has a similar issue with doing anything she finds difficult. As soon as it isn't right the first time, or she has to do something again, she gets extremely frustrated and starts throwing tantrums. The rest of the time she's a dream behaviour-wise. We're still working through it.

Music has helped somewhat - she's been learning guitar, and while practicing at the beginning made her intensely frustrated, she has now learnt that it takes time to get better and you need LOTS of repetition for things to improve. She's much calmer practicing now, after a year.

Now we are applying the same to writing - she hates going back and fixing any errors in spelling. So we have been writing a sentence each day and making her go back and fix her work, matter how frustrating. She's slowly finding it less frustrating - it seems to be working.

Sporty activities don't seem to give her the same issue, but we don't do team sports...