Hi tinks I'm really sorry you're going through this it sounds incredibly stressful.
I'm not an expert on exclusions by any means (it might be worth posting in education as well?) but do have some experience in this area.
i don't think you're being unreasonable at all but I can also see, to some extent, the school's point of view. I think your best way forward at this point is to look at ways at working with the school to get the support you want for your son at school. The fixed term exclusion (the one and a half day) does seem a disproportionate and totally inappropriate response for a child who is relatively newly placed with adoptive family. However, as it is a fixed term exclusion and it has now passed there isn't much you can do about it. You can obviously complain to the governors and would be perfectly within your rights to do that but my advice would be don't waste your time and energy because what is it actually going to achieve? You may get an apology or acknowledgment from the school that they acted over zealously (to put it mildly) in issuing the exclusion but this won't get your son the support he needs. I worry you could end up wasting a lot of time and energy over the exclusion that could be better spent getting the school to get some decent support strategies in place. Use your energy to help school work out what they actually need to do to help your son.
Practical suggestions for school:
Training in attachment issues for all staff
Google 'Herts working with looked after pupils' and you should get a link to a useful doc from Herts LA giving some practical suggestions for school staff on supporting challenging behaviour of LAC pupils using the Dan Hughes PACE model
Look up BAAF pupil premium case studies and share with school. These have some good real life examples of how schools have used PP to support adopted children.
However, having said all this there are some red flags for me from the school. The bit about releasing extra funding seems weird. I have never heard of this 'emergency' funding. The school is entitled to PP for your son (currently £1900 per year) but this is only released to schools based on the January census numbers as far as I understand so your school may not have it yet. However, if they know he's adopted they know this money will be coming so I don't really understand what the extra funding is they're talking about. Do check with school they know to apply for pupil premium though (it sounds obvious but some schools don't know). As far I am aware there is no additional funding school can tap in to for pupils who've had a fixed term exclusion - otherwise all schools would be doing this surely?
Re using exclusion as a punishment. I wonder if the school wanted to send your son home to 'cool off' but had to officially record it as a fixed term exclusion as schools are not legally allowed to send pupils home to 'cool off'? Possibly. Regardless, school need to know that this type of punishment (along with time out and other 'shame' punishments) are particularly damaging for LAC pupils. Obviously they need to be punished if they do something wrong but school needs to look into 'time in' punishments rather than 'time out' ones which will just perpetuate feelings of inadequacy in traumatised children.
School needs to work with you on supporting your son to be successful at school. Don't be afraid (I'm sure you aren't) about speaking to SENCO, class teacher, head teacher etc as and when you need to. They will get extra funding via PP to support your son and don't be afraid to challenge them about how they are spending it.
To go back to exclusions. The guidance around issuing permanent exclusions (PEX) state that it must be avoided if at all possible for looked after pupils. This is because the DfE recognises the extra vulnerability these pupils have. Schools are expected to do absolutely everything they can to support LAC pupils so that they don't get to the point of PEX. I would argue that the same principle should apply to fixed term exclusions. Our children are very vulnerable. Being 'sent away' from somewhere (which is what the exclusion is doing) is likely to trigger intense emotions for them.
Re the excuse about needing to exclude because of the mark in the other child, I think this is a bit of a red herring on the part of the school. Yes, schools do have a duty (written in the exclusions guidance from the DfE) to ensure the safety and well being of the rest of the pupils, and not being able to ensure this is a reason oft used in exclusion cases. However, context is everything. In this case the mark was accidental, not premeditated or planned in anyway, and not, as far as we know, part of any persistent concerted pattern of misbehaviour towards this one child. In this context, I would say the mark is irrelevant and has been used by the school as an entirely spurious reason to justify their over zealous and inappropriate exclusion.
My advice would be to accept this fixed term exclusion. It's been and gone. But talk to the school about how it is an inappropriate first line punishment for your son going forward, you are keen to work with them on finding ways to use PP to support him, plus any other support he needs, and you think an alternative to exclusion might be XYZ (whatever you think would be appropriate, possibly internal exclusion where he goes to be with a member of staff one on one, or if he's really little, 'time in' with a specific member of staff)
The other thing is that if he's only been with you 3 months he may not be ready for school yet. I don't know how old he is but if one or both of you are still on adoption leave could you take him out of school, defer his start or something and focus on securing attachment without the distraction of school?
Apologies for the diatribe. Hopefully something in all my ramblings might help you.