As an attendance officer at a primary school I can absolutely tell you this is unacceptable.
I would only ask for a proof of illness if the child has 90% attendance or below.
I would then accept a photo of said chicken pox and the child would be marked as ill.
We do routine home visits on day 3 and 7 of illness (for the children under 90%) and if we can see the child is ill, which is very obvious with chicken pox, again we would mark the child as ill.
I would demand a meeting with the head or phase lead, there is no need for the attendance team to be questioning you without good reason.
If you are unable to secure a meeting with the head I would write to the board of governors or if an academy the trustees.
Also bear in mind that is not the school that fines you, it is the local council. So as others have said keep a record of all your conversations, try to have all conversations written (email etc.) if possible and then if the council do fine you, you can raise a grievance with them.
The school are being completely unreasonable here.
I hope your daughter gets better soon.