Give Sammy and Payton a bath, which will cut down on dander, and then just don't let them into the room where Hugo sleeps.

The excema could be from anything, and may have something to do with the cats, and may not. It could be the soap you use, even baby soap has scents in it that can annoy sensitive skin. My family all has ridiculously sensitive skin, and my sister had terrible excema as a kid. Lady's Human also had excema when he was a kid, yet both of them have much, much, much milder asthma than I do as an adult.

The asthma is inherited, in our case, from both parents. As are our allergies.

Pediatricians often suspect pets first, when that may or may not be the allergen causing the problem.

My sister and mother could not (and sister still cannot) use soap. What?? You say? Ma swore by Pear's "soap" which is glycerine, not soap. My sister uses Lowilla.