One thing that I found interesting about some of the original description of what happened with Coley's DS's birthday is that the other two stepbrothers (who presumably have as large a gap in age, if not larger) responded enthusiastically to the reminder that DS's birthday was coming up. It was really only Jeff who reacted negatively.
I'm thinking, therefore, that the whole issue of whether Coley and her DH should be reminding his sons of her son's birthday is kind of a red herring. Clearly, they have at least some positive reinforcement for those reminders. It wouldn't surprise me if this is not the first time one of the three older sons has expressed gratitude at a reminder.
I also think that whether parents reminding their adult children about birthdays or significant events in others' lives is appreciated and/or appropriate is highly variable from one family to the next. I talked to my mom on Sunday, and she asked if I remembered that my sister's birthday is coming up. I'm almost 29, and have been living entirely on my own (and halfway across the country) for the past 7 years. I'm the weirdo in my family who not only knows the date of everyone's birthday, but also what year they were born. But my mom reminds me of my sister's and brother's birthdays most years because she knows they appreciate hearing from me, and I appreciate a little extra insurance against getting caught up and not realizing that the date I know is upon me. There is a difference between remembering that my sister's birthday is Feb. 10th, and connecting it with the Feb. 10th that is this Monday.
I actually think it's a red herring that Jeff's response occurred surrounding DS's birthday. It could have been any event. It happened to be DS's birthday because that was the first event that occurred after Christmas, which was the point when Jeff began expressing some irritation about gift-giving. DH didn't know Jeff had concerns about gift-giving in general.
It was either Rob or Shawn (I'm not sure which) who first contacted DH and asked if DS's birthday was coming up. That's what prompted DH to contact all three of them with the reminder. Per the bolded above, that's exactly the kind of thing that can happen and has happened in the past. Dates the older guys aren't familiar with may be overlooked. They seem to seek reminders from DH. DH didn't want DS's birthday to be overlooked, so he reminded the three of them. The gift to DS was an add-on, and in this case, was the straw the broke the camel's back for Jeff.
Jeff's response blew DH's hair back, particularly because it was prompted by DS's birthday. This wasn't the wedding of a distant cousin he hasn't seen for 5 years. This is his young stepbrother, who he says he loves and wants to have a relationship
with. From that standpoint, the conversation DH had with Jeff didn't make a lot of sense.
Going forward, I think the best we can do is clarify what information Jeff would prefer to have and how he would prefer to receive it. It would be simplest to give Jeff all the necessary dates, let him plug them into his calendar, and leave it at that. If he overlooks something, then that's his responsibility, and he can't complain if he forgets. If he wants us to give him a reminder, we can do that, but as Dindrane says, there can't be complaining or resentment about the reminder.
There's another theme in the OP though, and that's the idea of obligation surrounding gift-giving occasions. I can't quite get past the idea that Jeff resents giving gifts when certain occasions come up. I'm not speaking of DS's birthday there. I'm talking about all events, like weddings and births and graduations. From their conversation, DH seemed to think there was some entitlement in Jeff's attitude: an "I don't think I should have to." DH clarified that no one is required to give gifts; it's done because the giver wants to. If he doesn't want to, then he shouldn't.
If Jeff wants to acknowledge these occasions in a different way or in no way, it's up to Jeff to decide to live those values. If Jeff is having difficulty reconciling his feelings (i.e., he doesn't want to feel obligated but also feels guilty about not giving a gift), then that's for him to sort out.