It wasn't that I was tempted to "bash" your family, but I'll try to explain how "inbreeding" works and why it can potentially create disabled babies.
Basically, every human has two copies of the same gene. Often a dominant gene and a recessive gene. When two strangers have a baby, they have a total of 4 of the same genes (2 in each partner). This means the baby will receive one from the mother and one from the father. If one of the partners have a faulty gene and that gets passed onto the child, chances are the other partner will have a good copy of it so the child will have at least one good working copy of that gene.
When relatives procreate, say say siblings for example, the diversity on genes is limited. What that means is, because the siblings received their genes from the same parents they share 50% of their genes. So if they both have a defective copy and a good copy of the same gene, the chances that the baby will receive two defective copies increased.
Now, cousins share far far less than 50%. That's just a scientific fact that you would learn in 7th grade. So the chances of cousins having a defective baby are obviously less than siblings for example.
Now, if your family already had an increased amount of defective genes, they would have a higher chance of having disabled babies than cousins who had a very healthy gene pool.