Mumtodd, I really think it would be worth having a go at this, although I do agree that you won't see results in just a few days - 10 days to 2 weeks might be more like it. But imagine if it does really make the difference to your lo's eczema - you will be very pleased that you have established the cause.
An intolerance to cow's milk protein won't show up on skin-prick tests or RAST as it works in a different way to a classical allergy. Unfortunately this is one reason why medics often dismiss talk of intolerances as having no basis in reality.
My ds1 had really bad colic as a baby. He was fully breastfed up to about 8 months, but cutting out all cow's milk and cow's milk products in my diet really made a huge difference. Once I had cut it all out, just eating one yoghurt in the morning made him scream again in the evening. I am a scientist by training, so I wouldn't have reached this conclusion just on a whim (as many medics tried to imply). I tried to reintroduce cow's milk into my/his diet at various points and he always reacted to it - right up to about 4 years old. I am so glad we established this was the cause of his colic, otherwise he would have gone on being a miserable baby for ages. On talking to our parents, it emerged that both my dp and I had an intolerance to cow's milk as children and had been brought up on goat's milk - so perhaps we should have suspected this earlier. I would really advise you try cutting out cow's milk, especially given your dh's history.
I was also concerned about calcium intake but there is some really good advice on the vegan society pages, and we also saw a dietitian at the local hospital who gave us a handy way of working out calcium in his food. I used to make sure he had lots of bread (as he could tolerate this), hoummous, eggs, nuts, salmon or sardines and green leafy vegetables (luckily he loved broccoli) and we gave him calcium-fortified orange juice too. If necessary you can use liquid calcium supplements but we didn't feel we needed to.
Although ds1 never had severe eczema, we have some friends whose ds1 did, and his condition also improved dramatically on a dairy-free diet. He grew out of it quicker than our ds - luckily, as someone at his nursery gave him a full glass of milk when he was about 1 yo .
If you want to learn more about food intolerances I would really recommend this book as it was my 'bible' through those difficult first years. And I notice that there's even an Amazon review from someone on the board of the National Eczema Society!
It is tough cutting out all foods with cow's milk in them - as magicmayhem and others have said, there are loads of foods containing milk - and I ended up making most of our food from scratch, which was probably healthier for all of us but could be very time-consuming for me. I still think it was well worth it.
apologies for the really long message