This sounds like what both my boys and myself have. When we go on vacations, one or all of us will break out into red rashy hive looking things after spending too much time in the sun. I don't know for sure about your, but ours is more of a heat rash, coupled with the wrong types of sunscreen. I tried multiple kinds on myself, before I even had kids. Finally I found a kind that was all organic-natural. That has helped me immensely. Then my boys each came along and they both have a tendency to get it too. I just try to keep them shaded as much as possible, or at least in the water if they are in the sun. The combination of water and shade helps. If they have to be in the direct sunlight, I try to keep them with shorts and tshirt and just put a very minimal amount of sunscreen on them. Since their faces get it first, I try to just put a dab on their cheeks, nose and ears - but mostly shade their faces with a large-rimmed fishing hat. Benedryl also helps us though, because it calms down the rash, as well as cool baths and clear colored aloe gel (not aloe based lotions or colored aloe gels).
I also found out that my father had this quite a bit when he was younger and still breaks out with it if he is outside for prolonged periods of time with suntan lotion on (ie -- by the pool on vacation TRYING to get a tan). It seems the combination of heat, sun and most lotions causes our family to break out in rashes. FUN, FUN.
I hope this helps - if not, I hope you find a cause and cure quickly. Kids love sun - its hard to keep them inside, isn't it? :) Best wishes, B.