I don’t think that teachers should tell their spouse - or friends - anything about their pupils in a way that identifies the pupil. But I know some do.
DC1 was diagnosed with ASD a few years back, obviously his primary school and class teacher Mrs Smith* were aware he was being assessed, and of course once he had received a diagnosis the school were told about that.
Shortly after this, I was chatting to another mum in the school playground (whose DC was in a different year group to DC1), and I told her that DC1 had recently been diagnosed with ASD.
And she said “oh, I know, Mrs Smith told me all about that when we were out at the weekend”. 
Turns out other mum was good friends with Mrs Smith so saw lots of Mrs Smith outside school.
I let it go at the time, because I was thinking that well, we weren’t trying to keep it a secret, but in retrospect I really should have said something to the head teacher.
The other mum had absolutely no need to know about DC1’s ASD diagnosis, she didn’t work at the school, or even in any area related to ASD / SEN, so it was purely gossip on Mrs Smith’s part.
It did make me wonder what else Mrs Smith was telling people about the kids in her class.
*teacher’s name has been changed