All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
You are not sinful for giving birth to children who are affected by the same disease. It is Allaah Who predestined your children to be infected by the disease, as He tries His Slaves with whatever He wills. Therefore, a person is not sinful for things in which he has no choice and which are predestined and decreed by Allaah.
As regards birth control, if the situation is as you mentioned that the possibility of contaminating the children with the disease is highly probable, then it is permissible to stop giving birth temporarily by using birth control pills or by resorting to coitus interrupts. For more benefit, please refer to Fatwa 84240.
As regards permanent birth control, then we do not consider that it is permissible just for the above-mentioned reason. Allaah Says (what means): {And when he goes away, he strives throughout the land to cause corruption therein and destroy crops and animals. And Allaah does not like corruption.}[Quran 2:205] There is no doubt that sealing the fallopian tubes is preventing the reproduction and permanently putting an end to the possibility of having more children.
Finally, we ask Allaah with His Beautiful Names and Attributes to cure you all from every disease and to bless you and us with good health.
Allaah Knows best.