Ames, whilst I do not wish to comment personally on this subject, please allow me to reply to your post.
A school that has no public funding and is all fee paying may be selective on whatever they wish on the basis that if the parent does not like the rules or wish to abide by them as set up by the Govenors, Trustees and Hanholoh of the school then the parents may wish to look for another school. This may include uniform or no uniform, parents’ dress mode etc.
Your post uses the words ‘Even though’ which are ususally used to justify something. Please forgive me for being out of place here but these words signify to me that you are justifying the use of your laptop when your child is 3 years of age. Please bear in mind there are many children aged three who can well use a computer nowadays!
You may be using your laptop for work only but I think the school is trying to set a principle. Whilst many people claim their computer is for work only many will use it for online shopping, looking up information or whatever.
It is difficult enough to run a school but it is up to the parents who select that particular school to abide by the rules set up. Whatever the rules.
Thank you and apologies if I have caused any offense by my reply