Thanks for coming back and answering our questions, grandma! And for being so open and honest about what has occurred. I think WWU's posts make a lot of good sense, even if some of it may be hard to accept. I'm not sure if "adoption issues," sadly, are a major problem here, in addition to the other ones or if, as WWU suggests, DIL and her mom are using that (how obnoxious!) as a response to the other problems - but clearly, IMO, other issues do exist.
If it's any comfort, from reading on these boards, I know that some of these issues are very common. Many parents, today, are less tolerant/even less tolerant of GPs just "dropping over" or inviting themselves over than we were, years ago. (Even back then, I didn't like "drop-ins" and DH was very unnerved the couple of times my mom showed up unannounced.) So, IMO, it's not unusual that DS (dear son) and DIL expect that you only come over if invited. And it doesn't , necessarily, have anything to do with the fact that DS was adopted.
Nor is it unusual for GPs not to see their new GC all that often, during the early months of life. Now that dads tend to pitch in more, new moms don't seem to need as many extra hands. And so, having guests - even if "family" - is often just seen as another chore, rather than a help. Since DIL has criticized the way you feed and burp baby, etc., I'm guessing that you tend, with the best of intentions, to offer such help when you visit - and that she just doesn't want/feel the need for it.
Also, I'm wondering how often you saw DS and DIL b4 baby was born? GPs often expect that the number and/or frequency of visits will increase after the arrival of a baby. And sometimes, they do. But many young parents, today, expect, to the contrary, that once the GPs get to "meet and greet" the new baby, visits will go back to how they were, previously. If you only saw DS and DIL, once every few months, or less, b4 baby's arrival, for better or worse, that may be as often as they're planning/expecting to see you now.
I appreciate, of course, the fact that you were in "maternity/well baby nursing for 15 years." But I'm not clear on whether that's ongoing or in the past. If it's in the past, some of what you "know" may have changed since then. But even if it's ongoing, if your methods conflict with what DIL has read/been told/ just feels more comfortable with, then she's going to ask you to do it differently. I hope she showed you what she'd like, instead of crying out, "No! You're doing it wrong!" But, either way, if you argued with her about it (and I hope you didn't), that might be another reason why you haven't been invited for a few months (maybe not, I'm just feeling around for possibilities). In the future, I agree with WWU that you would do better simply to follow DIL's wishes concerning her baby.
As for the shower, I think it's very odd that DIL's mom didn't invite you. And while a hostess has a right to invite whom she chooses, IME, people usually do include both GMs at a baby shower and I feel it was "bad form" not to. I know that must have hurt and I am very sorry about it.
It's also rude, of course, as WWU points out, to demand an invite to an event, no matter how much you (general) feel you "should" be included. No doubt, your "'hissy fit'" and the resulting tensions it must have caused between DIL and DS probably did not endear you to DIL and her mom. I understand why you felt and reacted as you did and that you may have felt you were standing up for yourself. But, unfortunately, as a result, you may have started off on a bad foot with them.
Ok, IDK if DIL's mom failed to invite you at first out of ignorance or stupidity regarding your standing as an adoptive mother or whether, as WWU speculated, the "adoption issue" arose in response to something you said in that fit. Either way, I think it was very wrong of them to "go there." But, unless I'm reading this wrong, it seems obvious to me that there were problems between you and DIL and/or you and her mom b4 baby was even born. Perhaps, as you say, yourself, your own "excitement" over the coming baby may have overwhelmed DIL (also not unheard-of - in fact, we hear it very often on this site). Or maybe it goes back further than that. You would know that better than I.
One other thought about DIL's interest in DS' bio mom - It may just interest her b/c this woman is part of her baby's history. Did she ever express any interest in her b4 baby came along? If not, that may mean it's just about family heritage or even medical history, etc. it may even be a reflection of her own excitement about baby and everything to do with baby.
Or not. But even if she is uncomfortable with the fact of adoption, the other issues here could still, perhaps, be dealt with, as WWU has suggested. Perhaps if you can smooth out your relationship with her - refrain from self-inviting (that is, if you ever have), avoid offering to feed, etc. baby and honor the parents'/DIL's wishes on all matters regarding baby, including how to hold, etc., don't lean on DS to change DIL's mind anything, no matter what - she'll begin to see, in time, that it doesn't matter if you're the bio mom or not - what matters is that you were the mom who was there for him and you're willing to adjust now to be part of their and baby's life.