OP firstly, I am sorry for your loss 
I'm in a similar position. I'm In a 4 month relationship and we each have a young adult daughter who is 'sensitive' to our dating.
Mine said she didn't want to know any details of my love life and his said the same. However, we've both refused to hide it completely. I'm not having an affair and am not going to behave as if I am!
I told DD I was seeing someone and I really liked him but said nothing more. A few weeks later she asked me if I was still seeing him. A little while later she asked his name and a few details. The other day she saw his picture on my screen saver and was was fine.
Similar has happened in his household. His daughter even asked to see my photo the other day and I'm now being mentioned in general conversation with 'I like the sound of her' being said quite regularly 😁
I think letting the DD's curiosity set the pace has been really beneficial and setting the scene earlier rather than later has made this possible.
His daughter and s now starting to make noises about meeting me. It's still a way off for mine but she says she'd be ok with it at some stage (she volunteers this, I've not asked 🤷♀️)
I can't help but think you are absolutely right to be concerned as by now I'd really be expecting him to at least start to lay the foundations of introducing the idea of you I.e deliberately turning the laptop when his DD walks into the room; receiving a text with a verbal laugh and an obvious grin as he's typing a response.
Both of my kids asked ME if I was dating rather than me broach it with them because I set it up that way. Almost what he seems to be hoping for but with a bit of engineering on my part and a bit less jarring than seeing me with DP in the street! He obviously doesn't want to hurt her so the onus is surely on him to step up and ease things gently for her!