PE --
I have very little advice regarding the nipple shields as I have no experience with them. However, it sounds like you are doing everything you can! It sounds like an exhausting and gut wrenching situation.
Please trust that you are doing everything right -- even down to giving the formula. Don't beat yourself up. You are only trying to do what is needed for your baby and she needs to be fed.
I agree with CO that she is probably just frustrated at having to work so hard for the milk. When I got pg and was still EBF my DS, my let down took ages and my supply dropped a bit. We went through a few very difficult weeks of frustration until he adjusted to it. He was always (still is with solids) very serious about his food and wanted lots of it. He would also get VERY frustrated at the boob during growth spurts. He would squirm and scream and even punch, yes PUNCH, my boobs in frustration when the flow got too slow. My DH used to encourage me to give him a bottle. This was always my answer:
He has to work it out at the boob!
I always stuck by that it and it was probably one of the smartest things I ever did. No matter how frustrated he got, I just kept offering him the breast. Eventually (hours, days, weeks) he would always settle down. But I remember more than once, clearly, sitting on the couch with a screaming, squriming, hungry baby in my arms, trying to get him to latch and stay latched to a slow flow. It was hard. You can do it... I know you can!
ZOZO--
Please don't beat yourself up for listening to the docs. Of course that is what you did!
From the sounds of it, this is more a confidence issue than anything else. Your wife just doesn't know to trust her body and what it will supply yet. That confidence is hard to learn in the beginning (meaning for the first 6 months!) Everytime my DS went through a growth spurt, I was worried he wasn't getting enough (see above for description of what he would do.) But, in the end, my body always caught up and supplied him with what he needed.
I firmly believe that the only way your wife will gain that confidence is to cut out the formula. Just bite the bullet and do it. In a couple of weeks, she will see that your baby will have gained weight without formula and that will start to build her confidence.
As for twisting the nipple, the frustated guess would also be my guess. Especially if it is toward the end of a feed. The flow slows down and babies that are partly bottle fed can get very frustrated by that (it doesn't happen with a bottle). That is what is called "nipple confusion." Nipple confusion isn't that they are confused about how to get milk out of one kind of nipple -- it is that they get frustrated by the slower flow and harder work of a breast and "want" the bottle. That would be another reason to cut out the bottles of formula. It will elminate the nipple confusion.
Also make sure baby is positioned properly in whatever hold your wife uses:
This is a good cradle hold: See how the baby is tummy to tummy, spine straight. They shouldn't have to turn their head to access the nipple. They should actually be laying on one arm/shoulder, not their back. So totally on their side.
https://www.smartparenting.com.ph/images/site-alpha/articles/child-care/breastfeeding/breastfeeding_basics/6_breastfeeding_positions/Picture1_BIG.jpg
This is a good cross-cradle: The baby is positioned the same as the cradle, but up against mom's side (opposite to the breast that is being offered) a bit more. And mom's arms are positioned differently to hold baby. This one often works well for women who have larger breasts.
https://www.womenshealth.gov/breastfeeding/images/box-cross-cradle-hold.gif
This is a good football/rugby hold: Have the baby supported on pillows or a nursing cushion. Again, the baby is on it's side and the spine is straight.
This is a good side by side: Again, baby is on it's side and straight. This one is harder to master for most women and takes practice. Baby usually needs elevated a little to get a good latch. I found with my DD that swaddling her tight helps her side-by-side nursing position. Ladies with larger breasts often find they need to position baby's head on their arm (not sure exactly how this works as I have only seen it described, it is not a problem I have.
)
https://www.lpch.org/media/images/conditions/ei_0006.jpg
This is good of the cross-cradle using a nursing pillow:
https://images.meredith.com/ab/images/2007/12/m_101138718.jpg
Remember, good positioning is key. It will make everything easier and more comfortable for mom and baby. Some babies are more picky about position, too. For example, my DS could nurse well even when positioning was very "sloppy." My DD is not that way. She gets a bad latch, pops off, and/or gets frustrated at the slightest shift in position. She will also have a bad latch and get frustrated if the position isn't just right for her. And only a teeny tiny shift in direction of my or her body will throw her off. Have your wife experiment with tiny little shifts and see if anything helps.
As for Fenugreek, I take it in pill form. Just do the research to make sure she takes enough everyday. I found it took about a week to up my supply, other women it works for almost instantly. I should say that I don't NEED it.. but take it so that my supply stays MORE than what my 2 kids eat per day. I pump and freeze the extra to build up a good freezer stash.
Come back if you have any other concerns!