Food, meds, and supplements can all interfere with any kind of iron. Which is why my daughter takes it only with orange juice, because the vitamin C will, as CH said, boost iron absorption.
Whichever brand you try - give it about a month, then have labs done to check iron status. The most important iron lab test is "ferritin" - second most important is "hemoglobin" and third in importance is "serum iron."
www.labtestsonline.org makes it easy for you to find out which labs are required, and what the lab results mean. You can insist on copies of all lab reports, especially the one that the doc says shows she is anemic. This way, when you get another test done, you can compare the two and see whether her ferritin (otherwise known as iron storage) or hemoglobin improved.