Giving my input. I haven't taken my kids to a funeral, mine are 5 and 10, they've lost two grandparents.
My 10 year old had the choice when my Dad died and chose not to, and was younger when it was my MIL so we didn't ask him.
However, in the days between my Dad's death and the funeral, he was around us all, at all times. I don't believe she should have had her Mum down to look after the kids as some have said, but I do believe she and the kids should have gone straight to Rob when he was home, he'll want to be with his children surely? I know when it was my Dad I needed my kids around, especially my eldest, he was my "normal".
I would not have been worried about routine, they should have been out of school and straight there, they're grieving too. She's such a selfish twit! But Rob should have been insisting they go there, if he hasn't it says so much about their marriage!