Frootloop -
I do think you're right and your cousin needs to hear about the misinformation that her HCPs have given her. I had a m/c a few years ago, and I know that no matter how many people tell you it's "not your fault," it's hard to believe that sometimes .... I still wonder whether the cold medicine I took during the first month, was what caused our baby not to develop correctly ("blighted ovum," never developed a heart beat). Despite being told that it was probably completely unrelated to that. So, it has to be awful, when the mom is already feeling guilty/blaming herself, to have persons of authority essentially TELL her that she's killed her baby.

If you do decide to be a bit more "circular" in your approach (i.e., your mom has a hissy when you tell her that you plan to talk to your cousin) -- depending on your particular age/circumstances (and your cousin's), you may want to figure out a way to bring that information up, in conversation, with your cousin at the next family gathering. If you and she are both bf and supportive of each other in that - maybe finagle the conversation to bf in general ("It's so great that you made it to the AAP minimum with your dd! Society makes that so difficult for us") -- and then slip in a scenario:
"You know, I just can't believe how misinformed some people still are - even doctors! A mom in my playgroup had a m/c a few months ago, and her Ped told her it was because she was still bfing. Her OB was furious that her Ped was giving her that old wives' tale still -- she's been looking for an new Ped. She'd researched online before getting pregnant, and knew all her stuff but it's so hard when you miscarry and you feel so much pain and guilt, and to have someone tell her something so awful ....!"
I don't know, it might be too heavy-handed - but if you feel that a direct conversation would be too rough on cousin/your mom, this might work? Unless she would see through your story, which would be far, far worse because then she'd have to wonder who ELSE knows.
Very few people know about our m/c. It's not something we've wanted to discuss. If she knows about yours, though, and you're able to start a dialogue with her, that might be really healthy.
The only other thought I have is, if she's from a small town, you could just mail information (cited medical research) to all the OBs/Peds there. For instance, there are only 2 OBs and 2 Peds in my town. A cover letter with some research information couldn't hurt, I'd think, in that sort of a situation. Who knows if they'd READ it .... I think my Ped and OB would flip through it at least, but then again, they're awesome and I hear awful stories about some OBs/Peds (as in the OP).
I really hope you're able to figure out a kind, compassionate way to help your cousin find out the truth (that she didn't cause her m/c, and that her HCPs are ill-informed) - and that she finds new HCPs for her family. And you're right, it's beyond lactivism for her situation - it's about healing.