We don't really know exactly when Christine died, but Glenn implies in court that she has already passed by that point (by saying her name *was* Christine). Glenn is 36 (I think.) in S1 (well. at the start of it), which is already somewhat young to have lost a parent, however it's doubtful that her death would have been after or any time soon before Morgan's death (~6 yrs prior to S1), as this surely would have been important enough insofar as it would have affected Glenn's psyche that it would have come up at some point or another. He couldn't have been that young when she passed, either, since he recalls "spending a lot of time with his mom"– at least as a kid when his parents had already separated– but there's a fairly large window of time left, stretching roughly from somewhere during Glenn's teenage years to his mid twenties, during which Christine is most likely to have passed away. The exact point in time is not particularly important, I'm mostly just trying to offer some perspective on the fact that Glenn can reasonably be assumed to have lost his mom when he was pretty dang young (but old enough to remember her well).
Of course there's never an easy time to lose a parent, but what I'm here to suggest– not as irrefutable fact but as dearly held and hopefully grounded headcanon– is that Christine's death was Glenn's first major experience with grief and, more importantly, with not knowing how to grieve. And why would he? His mother is dead, he likely doesn't have any friends who have gone through this sort of loss yet, and Bill Close of all people is not going to be the emotional support that his child needs, not only because he hasn't been with Christine for a long time, but because he is absent in every sense of the word and as Glenn says himself:
So Glenn loses his mom and what he learns implicitly from trudging his way through that experience is that the normal way to deal with loss is to Not Talk About It, a lesson he carries with him into every subsequent loss; of Morgan, of course, but also of Nick. To the former, this inability to voice the immense weight on his heart in turn imprints a similar effect on Nick. Not out of any desire to do so! Nor out of a lack of understanding for what Nick is going through or will to do anything about it
But Glenn can't help Nick grieve, because he doesn't know how to, either, all he knows is Don't Talk About It. It's not for nothing that Freddie suggested in Talking Dad that he would have imagined the ending to Glenn and Nick's arc consisting of the two of them visiting Morgan's grave.
As for the loss of Nick (/Nicholas in a different sense) while the pattern persists overall, there is otherwise a very interesting phenomenon that occurs with Glenn, as embedded in small and otherwise inconspicuous moments like these.
The attempt is clumsy, but clear: Glenn is trying to talk about it. He is trying to grieve! He's trying to do things differently! The pitiful responses of the other dads are unfortunately pretty emotionally constipated ones, for the most part, so the potential latent here largely goes unrealized, but I think it's meaningful all the same, and part of what makes Glenn's character so god damn good.