[WhisperingSilence]

I am gonna be a little blunt and to the point here,
The teacher asked you numerous times during the lesson to stop what you were doing, and you chose to not listen and to continue to behave in a way that was probably disrupting the lesson and stopping the learning of your classmates.
If the school policy is that after 3 detentions during one term and then you get a Saturday detention, while you may not like it, that is the school policy and I highly doubt the teacher who was doing the Saturday detention wanted to be there any more than you did.

I think you need to take this a lesson learnt and hopefully not do it again, as for your mum - I can remember being at school and like getting one like 15 min detention after school and mum finding out and grounding me for a week because the detention was for not having the correct p.e. kit despite me explaining to the p.e teacher that my p.e. shorts had been stolen from my p.e. bag. I still had to serve the detention and I was still grounded for a week.
I think your mum has dealt with the situation fairly.
The solution here is to maybe look at your behaviour at school and get less detentions then this won't happen again.