When two siblings in a heap are equal, how do you bubble down? I have a heap where both child nodes of the root are 10, and I'd like to perform an operation to remove the min value 9.

I proceed to replacing the root with its next of kin, 18. However when I bubble down, I am unsure of which direction to take.
Picking either should work. The heap property (assuming you have changed it to mean parent $\le$ children) will not be violated.