When the teacher told you about these difficulties your DD appears to be having at school, what was your response at the time? Did you ask how you could help her at home? Did you ask how the teacher and school were supporting your DD to ensure she doesn't get left behind.
In the meeting was there anything positive at all?
To be fair, the things you mention are not really serious issues. Many of them are very, very normal for a 4y child in reception. Not being able to write their name is not a real problem, it is something they can work on in reception. Struggling to recognse and write a number at this point is also not a serious problem.
Holding her pen wrong - well, it is good that this is brought up now tbh. Pencil grip is important later on, esp for curseive joined up writing. And pencil grip quickly becomes secnd nature. If not corrected now then it becomes far more difficult to correct later on. I know - my 9y DD has an odd pencil grip and it does affect her writing, but at 9y it is almost impossible to correct - and we have been trying for a few years now!
You say the teacher was mocking your DD - in what way?
The teacher's appearance is irrelevant right now and tbh doesn't help your op, but ignoring that now, how does your DD feel about her school?
If the teacher has really been mocking a child who is struggling then this is pretty serious and ought to be reported to her line manager for unprofessional conduct.
If you don't feel the 10 minutes appointment is long enough to discuss your DD then ask the teacher for another appointment, a long one, maybe after school one day. If you are concerned about the teacher's attitude at another appointment take someone with you to the appointment.
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crabapple - ill children should not be at school if they are ill. Slight coughs and colds - yes, feeling poorly, temperatures, etc - no. Please do not send ill children to school - the staff would rather not end up ill themselves (absent staff is far mroe disrptive than to a class after all) and the rest of the children may end up ill too. Not good.