Sorry to hear about your in-laws attitude. It does seem surprisingly common, from what I've heard. Luckily mine have been fine, though they live a long way away so we only see them a few times a year (it was only once a year before DH died as we lived so far away).
I don't really know how the children feel about being asked about their dad, as most of the time it's when I'm not there - though I do remember in the fairly early days the mother of one of DS's friends did apologise to me for upsetting DS when he had gone round to lunch - she didn't know, and had asked about DH, and DS had ended up in tears.
We had to move countries after DH's death so they started new school and nursery, and I made a point of giving the teachers the relevant background, but I don't think they would necessarily broadcast that to the other children. In a way I felt it was better for the children (and me, for that matter) to start making friends just as themselves, rather than immediately being labelled as 'the ones whose dad died', as too much sympathy and pity can be hard to deal with.
I think they do sometimes talk about their dad to their friends - they certainly like talking about him to family and people who knew him - but I have the feeling that (like me) they don't like being caught by surprise and having to explain yet again. But once one friend/friend's mum knows, word seems to get passed around fairly quickly within that particular social group, which makes it a bit easier.