Is it permissible for me to ask my ex-husband to double the child support for my son, knowing that he will likely refuse to see the child in return, and would I be sinful for this? And what can I do to overcome my intense grief upon learning that my ex-husband is the son of zina (fornication/adultery), and the resulting feeling of distress towards my son?

The visitation of the child is a right for both parents, and the custodial parent is not permitted to prevent the other from visiting. As for the child's maintenance, if the mother waived it for the husband in exchange for the divorce, then it is not incumbent upon him, and the mother has no right to sue him for an increase. The mother is not permitted to discuss the marriage of the husband's parents, as such talk may constitute slander. If the marriage was without a guardian, the child is still attributed to him. And assuming the husband was a child born out of wedlock, he bears no sin for that, and he is not held accountable for the transgression of another.