With their low birth rate and conservative attitudes I'd think the dwarves would be very pro-life. They might make an exception for half-orcs due to their hatred of them, but I'd lean as a DM more towards not permitting it by their laws.
The child would grow up ostracized, with no friends and nothing but contempt from the vast majority of dwarves. As soon as it was physically able to survive on its own it would probably leave on its own volition or tossed out of by the others.
I actually think it would make a great PC or villian.
about 3 levels later was gang raped by the other two characters-by choice,no magical compelling.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.