Yep- sounds like eczema to me, too. The fragrance free detergents are important, and don't use dryer sheets or fabric softener. These irritate skin. As another poster mentioned, keeping the skin hydrated is a BIG preventative for eczema breakouts, and this needs to be done RIGHT after getting out of the tub. I'm allergic to lanolin, so we only use petroleum jelly.
Also, keep in mind that some kids have eczema flares in the summer, some in the winter. Using sunscreen on a regular basis seems to irritate my daughter's eczema, but that doesn't stop us from using sunscreen!
Try dressing the baby in cotton clothes because they breathe better, and maybe have a fan going to make sure he's not overheating. I'm glad I had winter babies, because I'm sure I would have overdressed my two kids in the summer! LOL
Good luck and good for your daughter on seeking another doc's opinion. We mothers are dismissed too many times by docs when we have valid concerns. My sister is a nurse practicioner in dermatology and she says that you wouldn't believe some of the cases she's seen that ped's have tried to diagnose and treat themselves.