God's will and genetics

In the Deseret Morning News this morning, there is a story about a fairly brutal genetic disease becoming less rare in the twin FLDS cities of Hildale and Colorado City.:

Until a few years ago, scientists knew of only 13 cases of Fumarase Deficiency in the entire world. [Arizona state doctor]Tarby said he's now aware of 20 more victims, all within a few blocks of each other on the Utah-Arizona border.
The children live in the polygamist community once known as Short Creek that is now incorporated as the twin towns of Hildale, Utah, and Colorado City, Ariz. Tarby believes the recessive gene for Fumarase Deficiency was introduced to the community by one of its early polygamist founders...
...Tarby said the early founder who brought the recessive gene into the community had numerous children, so copies of the gene were passed on to children and grandchildren. When cousins or other close relatives marry, two copies of the gene can be passed on to a single child, triggering the disease.

Apparently the marriage of relatives is common in the FLDS church. Because of the religious environment, this isn't likely to change. The families of those afflicted with Fumarase Deficiency are very patient and caring:

..."I've seen some children that can talk and communicate a little," Wyler [Former FLDS member, related to some of the victims of the disease] said. "And I've seen others that are totally laid out. They have no movement. They can't do anything by themselves. Literally, if they're 8 years old, it's like taking care of a baby."
...Tarby said children suffering from Fumarase Deficiency have unusual facial features and frequent "grand mal" epileptic seizures. The children require constant care from parents and close relatives. "In some ways, they are really kind of remarkable people," Tarby said. "They do treat these kids pretty well."
Wyler agreed that the parents and close relatives are loving caregivers. He said it's partly because they believe it's a calling from God. "They would just assume they've been given a test and they need to pass this test," Wyler said. "And it's their lot in life to take care of a child like this. And they'll give it everything they've got. And they'll do a good job. Very good job."

One of my nightmares right now is having a severely disabled child--I know there is a lot of heartache associated with that. And the amount of patience and faith it takes to "do a good job" in that situation--it has to be huge. Accepting God's will in matters of health is something I'm dealing with in my own family, on a much smaller and less tragic scale. I truly admire those who have worked through those issues and come through with their faith intact.

And yet I am concerned. I realize that if it was God's will, the recessive genes that create this disease could be "disable", or not linked up so that they are both in the child's DNA. However, aren't we required to do all that we can to help ourselves as well as asking God to help us? I wonder if marrying your cousin or aunt or niece or whatever is a little like rejecting medical help when your child has pneumonia. Yes, God could cure the pneumonia, and without doctors. But it seems to me the more knowledge we have been given (and have access to) the more responsibility rests on us. We can't always expect God to fix our "mistakes"* when we have the ability to fix them, or at least not risk them in the first place.

*I am not calling these sick children a mistake. However, now that it is known that the risk exists, if you have reason to believe that you have this recessive gene, and the person you marry has much the same ancestry, then I think it at least a great risk, and possibly a mistake, to blithely procreate without considering the hazards.