Aw bless. My ds2 has terrible excema too, and we have to be really careful about swimming. I find that it helps to cover him in vaseline (which is water resistant) first, although it does make him very slippy/ hard to hold.
I was recently advised not to put any other creams onto him before swimming, as the chlorine identifies them as impurities and so attacks the cream/skin beneath, which makes sense.
We have been lucky enough to find a local pool which uses salt rather than chlorine which is wonderful.
Our boys have shared baths but on the understanding that it is with water only, no soap or bubbles. They are fine that way - we just have dozens of bath toys to play with instead of bubbles (and I have to wash the bath out with loads of clean water to remove shampoo residue, or else he has an awful flare up.
As a matter of interest, we took ds2 swimming in the sea when he was tiny - and it did more to help his excema than anything else has ever done - worth waiting until summer for though! (We went to Studland bay/Swansea in Dorset. It was perfect - shallow beaches with almost no waves. He spent hours, sitting, wandering about in the water, and his skin changed overnight.)