I have been wondering the very same thing about what happened to these people. I too can find no death record for my internee, Peter KREIN; he simply disappears. I have checked all through 1837online up to where he would not have been living any longer, and cannot find him; he was older than many - almost 50 when WW1 began - so I wouldn't have thought he would have had much stamina or ambition for starting over in America, especially considering all that he'd been through already, including being widowed twice and losing some children. It's also worth checking with the Commonwealth War Graves Commission for a death; they do not list the internees on their website, but they do have records, as they come more or less under the category of POWs - IF they died while interned; I wrote to them, but they did not have my man. In my case, he also had a young English-born son, and I can't find him either; he didn't die young, but I find him nowhere.
To answer your question specifically, I am not aware of the British-born children being labelled enemy aliens, perhaps simply because they were children and were not capable of aiding and abetting the enemy, so not considered a threat. I guess a spouse was seen to be subject to direction by her husband, since it was usually a husband who was interned - the vast majority of German immigrants had been single males in the 19thC.
Ultimately, the Red Cross archives in Geneva are the place to look apparently, because these camps and internees were monitored and helped by Red Cross. but I'm not sure if access is allowed; it might be that you have to pay their researchers. It would be expensive, as I read that their archives are in a mess.
Also, the Anglo-German Family History Society has some lists, but I have not yet seen them.
You're quite right that at least 3 generations were affected. I think more, actually, because it messed up the future family dynamics as well, which I can demonstrate in my own situation.
I live in Canada. Interestingly, a few weeks ago, the Canadian government came close to apologizing to the Italians whom it interned. They won't actually apologize, because that would make them legally liable, but they came as close as they could. Someone tell me if I'm wrong, but it's my sense that the "climate" in Britain wouldn't allow that right now.
If you are living in a large centre with good libraries, please check out my bibliography on the subject (link is earlier on this thread). The book by Bird documents the fact that they were forbidden to change their names, for example. Anything by Panayi is particularly well researched.
I should also mention, in case you didn't know, that a large number of internees were deported after WW1. I have some info on that if you want, but not names. They were sent back to the continent.