Javotte, don't cry. Remember how LITTLE he is, and how BIG you are. He is so little! His anger is so powerless! Please keep that in mind always. Your job is to carry his discomfort and pain (being told off) when he is still too small to carry it himself. Please always remember this.
I got this from Penelope Leach: the best mother and baby book ever.
So, my answer to that would be:
You are such a cross little boy right now, so angry with Mummy. But don't worry, I still love you and I will still be here when you stop being cross.
[I HATE YOU MUMMY!] 'That's all right, I love you enough for both of us (and I will still be here when you need a cuddle)'
I reassure you this is how I dealt w my small people it stopped quite quickly and they are now ANGELIC teenagers.
Don't be so small that you are offended, and please don't shame them. Just be calm and loving.
(and revise the home schooling thing. Whilst I agree that education isn't all that, the socialisation of school is vital).