Totally normal to say 'your grown-ups' or 'your family' (we often get 'your family at home').
My daughter goes to a very tiny rural primary school, in a very non-diverse bit of Yorkshire, where there are about 40 families. The vast majority have a mum and a dad, but there are two single mums and there's my DD who has two mums. Honestly, if the teachers there can manage it, anyone can! Recently we got a Valentine's card addressed to 'my mummys' (and she's 4, so someone had to do some guiding to get her to write it).
This article is just trying to create a problem. I'm sure most schools are simply trying to be inclusive.