Sorry, this is kind of long.
My thoughts: First, if I understood your posts, I do think it was pushy of you to "ask directly" if your child could attend one part of the wedding festivities when you'd already been told no. In the future, I would not do that. If you have any questions pertaining to social events on your partner's side, have him do it. It's just a better look. And if the asking is really trying to get them to make an exception, just don't. However, even if you did make a little social error or two, we all do. It's not the end of the world or anything unforgiveable.
Second, if I can say this right, I think it's common that the person who is with someone in what we might consider a somewhat "gray area," informally, not married, with a child that is not the partner's, etc. feels that their standing in the partner's family is or should be more substantial than the family considers it to be at that point in time.
I think this part is not usually intended as a slight from the partner's family or friends. It's just that other people don't know what's in you and your partner's hearts, they just tend to not be that involved in your lives and think about other relationships more by the outer trappings. And of course they've probably also seen other boyfriends/girlfriends of the partner come and go. If/when the two of you are married, or together for a longer time, then they'll likely mentally categorize you differently.
If it applies, I recall being on both sides of this whole issue more than once. Feeling like my guy and I were practically married and being disappointed to be treated more like I was someone he'd just met, by others, even after a couple/few years. And also, on the other side of it, feeling like someone else's "new" guy or gal was at that point still likely just a passing thing and being surprised to learn how serious the relationship was to them.
Also, I think many people just aren't very familiar with stepchildren (or "almost" step children). They may not consider steps, let alone "not quite steps," to be full members of their larger family and may not even realize they are expected to, or that full acceptance might be very much wanted, unless/until it's explained to them.
Okay, all that said, it seems you either made a social error here in assuming your son would be welcomed at the morning-after brunch or they caused a misunderstanding by not making it clear that it was more formal than it seems you expected, with specific invitations required.
Either way, personally, I think they could have been more damn gracious about it. To have a young woman crying and a little boy sitting there wondering why he's not welcome to go inside with everyone else and have a bite to eat... Gee, I'm tearing up a little just thinking about it. It's not pretty, is it.
But then, remember we don't know it from their point of view. For ex., it could be they'd already had other issues with uninvited guests and had appointed someone to only allowed those who were invited in, with nothing personal involved whatsoever, just an unfortunate misunderstanding.
Either way, I'm sorry you were publicly embarrassed and went through that. It sounds pretty awful.
From here, if it was me, I think I'd just drop it and try to mentally start over with his family as if it had never happened at all. A well meant social error on either side is not a crime. On their side, it will likely be forgotten if your future behavior shows them you're actually quite a polite and lovely person. I was going to suggest sending a text or email to the bride, apologizing for the misunderstanding but I think it's better to just let this one be left with nothing more said about it. Best wishes to you.