Re: Weight gain
I am so sorry that you and your baby have had such a rough start!
30 g (1 oz) of weight gain per day is fractionally on the high side for some babies, but I think that with a baby who has had such a difficult beginning, it's reasonable to want her to catch up.
Is baby always being weighed in the nude, using the same scale every time? When weight gain is such a concern, you want to be sure that proper technique is being followed.
The idea of pumping off some foremilk so that baby could get more hindmilk is not awful, but not necessarily great, either. In general, quantity of milk is far more important to weight gain than quality of milk. A baby will gain perfectly well- in some cases, exceptionally fast- on a diet of so-called "foremilk" alone. If pumping off more milk meant that your baby got the same amount of milk but it was richer in fat, then she could potentially gain a little faster. But if she's not yet a great nurser, then pumping off the foremilk could mean that she gets less milk overall, which is not going to be helpful.
One thing you might try is to weigh baby before and after feedings, using a scale that is accurate to the 1/10th of an oz. The hospital should have one. By subtracting the before from the after, you can gain a very accurate assessment of how much milk your baby took in while nursing. If it's close to 2 oz, there should be no need to supplement. If it's less than that, maybe supplements are necessary.
I can't comment on the let baby sleep/wake baby up issue. It seems to me that more nursing = more calories, and more nursing sessions can be very important when you have a small, sleepy, and/or premature newborn. But in your child's specific case... I think this is another reason the scale could be useful. At this point you don't know how much she gets when she nurses, and that amount would give you a better sense of what you need to do in terms of waking her.
If you are going to supplement, one avenue to try would be to supplement with "double cream" milk. You pump a bottle, let it sit, and when the cream separates out and floats to the top, you pour that into another bottle which is then fed to the baby.
Stay strong, mama!
Coolest thing my big girl said recently: "How can you tell the world is moving when you are standing on it?"
Coolest thing my little girl sang recently: "I love dat one-two pupples!"