Sorry to ask this but would the children have any health issues due to their DNA / genetics and the conflict of both. Bloody shame, not in any way their fault.
From a genetic perspective, there are a lot of conditions that are caused by recessive genes, meaning you need one from each parent. So if those conditions are present in a family, then there'd be an increased risk in children of such a relationship compared to the general population.
But if those conditions aren't present in the genes, then the risk simply isn't there and the children of such a relationship could be as healthy as anyone else in the general population. If it goes on for many generations in a limited gene pool that does have recessive trait conditions then it's more likely to cause problems. I can't even think off the top of my head of a condition that is from recessive genes...Some things on recessive genes are pretty ordinary things like red hair, but some things are a lot more serious. And people who are not related can carry the same recessive gene and their children have increased risk of the conditions or traits on those genes.
So there's a good chance that the children would be as healthy as anyone else.
NB. I'm not saying these things in defence of incest, but more to clarify that health problems are not a foregone conclusion.
Another thing here is that they were half-siblings. So let's say, for example, that there was a different father, and then a male child was born of such a pairing, the child would get an X chromosome from the mother and an unrelated Y-chromosome from the father. So that's just like a child of unrelated parents. But let's say for example that the parents had the same mother and a girl was born, and that gets a lot more complicated....
Let's say the grandmother is X1 X2 (because she has two X chromosomes)
And let's say both the male and the female have inherited the X1
Now if a coupling between these two results in a girl, she *might* inherit X1 from both parents, so she'd by X1X1, and that is a way that problems could crop up.
I have no idea how these two are related, I'm just giving general examples of how the genetics could theoretically combine, and how some combinations in offspring could be higher risk, but it's still not necessarily going to result in health problems in the offspring.
