M.B.
There's are alternatives to Rx sleep aids. The top one is melatonin as some of our bodies don't make enough of it - it's what tells our body it's time to sleep. Also, if you are low in basic minerals and nutrients that can contribute - for example magnesium is really important. Here's an article that lists the top supplements:
http://www.associatedcontent.com/article/535863/supplemen...
B vitamins are also important for sleep. Do you take a high quality multi? I found that I needed to take a prenatal and extra iron while breastfeeding my second son (and wish I'd known that with my first) - nursing gives the nutrients to the baby at the expense of the mother. Considering how close in age your two kids are, you may well be nutritionally depleted.
Also, regular exercise is really good for inducing higher quality sleep. So, if you don't have a regular exercise program (I know not likely when you have an infant :), you might consider getting back into one - that helps me a whole lot.
You are so right to be concerned about what the baby might be getting and it is so sad to pump and dump and have to use formula instead. Also, the side effects of ambien may make your daytimes worse. What sort of tests did the doctor run before Rxing the Ambien - have all your hormone levels been checked as well as making sure you're not anemic (that can also contribute to sleep problems). Also, taking the Ambien is going to make caring for your infant at nite almost impossible - the night time nursing actually is really, really important in the early days to build your milk supply and since your daughter was early, she likely will really benefit from breastfeeding.
And, on that topic, do they know the reasons your daughter was so early? I ask because my first son was in NICU and I had lots of issues prior to his birth and they never figured things out. In hindsight, I was undiagnosed celiac, which contributed to liver problems and nutritional deficiencies and I was hypothyroid. I didn't learn much of this till years later and would have suffered a whole let less if I had known these things. As, it turns out both my boys inherited my celiac genes and so they suffered for several years as well (both in terms of feel well and their behavior - i.e., tantrums and anger out of nowhere).
In short, my point is that things don't happen in isolation - i.e., there's a root to your sleep problem and taking the Ambien might help in the short term, but ideally if you can figure some things out now, you'll save yourself a whole lot of grief in the long run.