I suppose it is possible that Spike knew. That little exchange did seem pretty pointed.
Mostly, though, I don't think they wanted to deal with it until the episode that they pretty much set aside with the purpose of dealing with it.
And here's another thing. Presumably, relatives of Spike's victims are to be found in Sunnydale every once in awhile. We know he was active there in Season 2 and for a little while in Season 4. It probably doesn't strike Spike as anything strange that the son of his most recent slayer victim is in league with a slayer. So let's say Spike does know or at least suspect. What would you have Spike say or do? And when would you have him say or do it? There is no making up for killing someone's mom. But at least Robin can have the consolation of knowing that his mom died in the field. Her death was an occupational hazard. She wasn't a helpless victim; she could have taken Spike out. It's not like she was one of Spike's happy meals. Also, he sees Spike now working on the side of good. I don't know what Spike could tell Robin that Robin hasn't seen or can't see with his own eyes. "I'm sorry" just doesn't cut it.
The only thing he can do is exactly what he's doing -- help the slayer fight the good fight. If I were Spike, I don't know if I would have stopped to say, "By the way, yes, you're right; I killed your mum. This is her coat. Sorry about that." I mean, really, what does that accomplish? Also, it seems redundant after the "New York" exchange. Having a soul and fighting alongside Robin and Buffy and everyone else to defeat the First says a lot more than words ever could.