Your group sound like a great bunch of caring friends OP and are being treated very badly IMO.
If she’s struggling with MH or the baby has health issues, she or her partner could have dropped a text thanking you all for cards/presents and just giving a heads up that she’s taking some time out to heal/focus on baby and will be in touch when she’s ready rather than making a big drama of ignoring messages, shutting doors in faces, and not having basic manners so to make people worry about her.
She must know what you’re all like as you’ve been friends for so long and you say you’re close so why not say what’s going on?
She has her brother there (who would surely be concerned if her DH was being abusive or controlling, and the DH obviously isn’t trying to isolate her from family) and is OK to go out with work friends so I wouldn’t worry too much TBH.
It’s terrible behaviour after she felt OK to visit you the day you came out of hospital after having twins and is now being so precious about you all visiting after she had her baby and quite some time ago.
Did she feel that she wasn’t congratulated quickly enough or given enough attention leading up to the birth? I can only think she felt slighted or insulted by something said or done and is punishing you all for it?
Did anything happen/was said at the baby shower? Any meet ups just before the birth?
Women give birth every day, it’s been over 4 months, most would be happy to have good friends who are excited for them and keen to welcome the baby, even their children are in this case!
I’d just leave her to it and focus on the rest of the friendship group. I don’t think there much to worry about if she’s out and about and has family support.