I like the way the books are written. There are lots of "wow" words and you rarely see a character who simply "said" something: speech is delivered in kinaesthetic, vivd language.
Grammatically, it is fairly simple but with interesting, unexpected bits thrown in.
As to the TV cartoon - I've never seen it and I don't think my dc did.
As to TV during wet play ... some schools don't do a great deal of TV at all. Dd's last school did, which I will admit was one of the things I didn't like about it. So I think I'd not be happy about television being shown full stop.
As to the original dilemma of the OP - sadly, there isn't, really, that much you can do about it. Your children will realise that there are things that go on at school that don't happen at home, and adjust accordingly. For what it's worth, I seethed about television at school when dd was at her previous school. It was massively limited at home, seemed to happen at school all the time, and consequently we had huge arguments about screen time that I just didn't have with ds, who attended a different school (with very little television).