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My DIL gave birth to our grandson, and happily he is healthy.
But as I have anticipated, from everything I've read about the arrival of the gchild, she is just beginning to follow a predictable pattern of not allowing me to hold him.
She says she doesn't feel comfortable letting others take him when he's restless or not feeling well.
Which this does make sense, except that to her, it has been quite often.
Am I following that you all do get together, it's more that when you are all together, she doesn't want others holding the baby?
pwBPD (persons with BPD) often have high validation needs. We all have validation needs -- the need to be really understood, to have others "get" how we feel -- and pwBPD may have higher-than-normal needs there, plus fewer skills and resources to manage when they don't get that need met.
True emotional validation -- really getting where someone is coming from, truly and genuinely understanding why they might feel the way they feel -- can be a way to connect to others and build relationships. We don't have to agree that what they do out of those feelings makes sense, but we can really put in some effort to put ourselves in their shoes and figure out: if I were in that situation, feeling that way, what would that be like?
I think you're on to something here:
She says she doesn't feel comfortable letting others take him when he's restless or not feeling well.
Which this does make sense, except that to her, it has been quite often.
She may not have an accurate perception of if GS is truly restless or truly ill. Her perceptions may be heightened, or skewed, or more informed by her own feelings than by how GS is really doing.
But!
Imagine that you
truly thought your infant child was crying for you, or was unwell, or did a little better with you than others.
You would probably do something similar -- we all would.
That's emotional validation

We don't have to figure out if the other person's perceptions or lenses are accurate. We can relate to -- if we did really feel that, or really think that, it might make sense why they do what they do.
I wonder if you might be able to build a little bit of positive relating with DIL, through emotional validation?
Next time you are all together, and maybe you ask to hold GS, and she says "I just think he is too fussy and wants me", instead of personalizing it ("she's starting to withhold GS from me"), it'd be interesting to see what happened if you used emotional validation:
"You really care about him", or
"You really want the best for him, don't you", or
"I know if my baby were fussy, I'd want to hold him, too"
or something, in your own words and with a warm tone and body language, that says: "I get it -- anyone would be doing the same thing if they thought _____".
I think my overall thought is -- it's a good thing that you are all still getting together and the baby is at least around you (though she is perhaps overreacting to her skewed perceptions). Creating some understanding -- so maybe she can let down her defenses a bit -- could be a way to keep that relational door open, so instead of her seeing you as a threat ("Blackwing is trying to take my baby" -- emotional reasoning), she can experience you as someone who understands.
Of course, you know her best, so if something here is off base, let me know. Just some food for thought!