Obviously we haven't the school's point of view here, but I do think it rather sounds like someone is being officious and labelling you as troublesome, and then seeking to confirm their own prejudices. It doesn't sound very professional and the SS immediate dismissal response is the indicator for me here.
Can I just confirm that there is absolutely nothing the school can do in terms of reporting absence to the local authority with regard to fines and so on until the term after the child is five, as Snickers has said. Your child is attending school voluntarily at the moment. You don't need to provide them with any paperwork at all. I certainly wouldn't be taking paperwork in or providing 'proof' of anything if I were in this situation.
You might get a letter saying the school expects children who have taken up a place to attend school regularly, but they can't legally enforce anything (apart from taking away your place if for some reason you don't show up for more than a fortnight without communicating with them).
By the way, despite some posts on here, SS absolutely will not take any interest in whether children below the age of compulsory school attendance are turning up to school or not. There is no mechanism in law for them to do so. It would have to be on other grounds, e.g. child going missing, child walking to school alone at 4, young child always collected hours and hours late from school with no reason given, child turning up suffering from neglect, child turning up with injuries, child turning up complaining of abuse, child not wanting to leave school with carer, etc.
Sandy, the £10 is a Subject Access Request fee under the Data Protection Act, and anything highly confidential is usually redacted (struck out with a black marker pen).
Moving forwards I think it sounds like the relationship between you and the school has broken down and I am wondering if it is worth pulling your DD out and putting her into another one next academic year, and having a fresh start, if there's something else local. I also wonder whether the school is due a stiff letter. If you want me to draft something, DM me a timeline of events and I will try to help.