You've changed what you have said several times. You say she snapped 'I don't know' at your child but also said 'The teacher admitted snapping to the class. The LSA was able to confirm that she snapped and that she said she was in a bad mood.' And also that she told the class she was in a bad mood. So did she in fact snap at one child, or a class of children, or a group of children? If at one child why would she justify to an entire class of children - that makes no sense. I can absolutely see multiple children all asking a teaching different things at once and 'I don't know' being a way to halt the questions to allow things to be taken one at a time and that would then make sense to say to the class 'sorry, I'm in a bad mood'. One child, no, it makes no sense to address the class.
Additionally, and assuming for a moment it was directed only at DD, one thing teachers are taught when dealing with ND is to give short factual answers. I don't know is a short and factual answer. What you cannot know is what else was going on e.g.
- you say your child was polite. How do you know? Maybe the teacher was already dealing with another child and your DD was interrupting her repeatedly, albeit with 'excuse me miss'?
- maybe she was dealing with other children with seating issues first, due to their own issues and 'I don't know' was absolutely the correct answer in the moment. Maybe the best laid seating plan became unstuck when Kerry refused to sit next to Nicola and she was adjusting on the fly?
- you don't tell ND people to hang on (some can interpret it as literally needing to hold on to something like on a bus which would cause issues for some)
- you don't tell ND to wait a minute as again it can be taken incredibly literally and cause a melt down if the minute is not met
- maybe as they said 'I don't know' the teacher was looking across the room to the LSA for help not remembering if DD has to sit alone / by a window etc. and projected her voice loudly to get the attention of the LSA, not the DD?
IMO the LSA is the one who is responsible for ensuring a new child is helped as a priority, including liaising with the teacher ahead of time to find out what seat and I expect that a teacher may also. You say the LSA stepped in when "the teacher was struggling" - they should not have let it get to that point, when the LSA's literal role is to support ND to allow the teacher to get on with the rest of the class and getting children seated is likely priority 1.
Yes, there are better ways it could have been handled. Such as the LSA getting her settled before anyone else arrived at class after liaising with the teacher. Yes the teacher could have explained at length 'This class has assigned seats but until everyone is in their seat I don't know where there will be a space, I need you to stand there until everyone else has arrived, then I will see what space you can be assigned and tell you which one' but frankly, the complexity would have triggered some ND people.
Like it or not, your child is one of hundreds the teacher has to work with. And given there is an LSA in every class it also sounds like the teacher has many different needs they have to juggle as well. You are very clear the school doesn't have any behavioural issues when another poster suggested that- how on earth could you know? I have NEVER come across a school that doesn't have any issues - lots are very good at hiding them, but I can't name a single secondary school teacher (and I know many) who have not been sworn at, called names, been personally insulted about their appearance / sexuality/ age / weight etc. or in some instances been physically assaulted.