In difficult cases like this it is almost always more than one thing. If it was just one thing, then you would be on top of it. Did you get the tongue tie snipped? it is a minor procedure and very worthwhile getting done. The other thing I would like to suggest is that she has a cow’s milk protein intolerance. The hints are the eczema, cradle cap and the milk intolerance in the father’s family. The good thing is that, following the family history she will grow out of it - but the tough thing is she is a baby now, and likely to be affected in the same way her dad was. I would try to sought this out before she begins solids. I would suggest a milk free diet - but this has to be done in consultation with a HP- nothing you should try alone, but at the same time often very successful and not as hard as it sounds. I am happy to talk to you about this if you wish - pm me