What is a specific moral question which might make it difficult to accept the idea of moral relativism?
There is no way to answer this question in an objective way. The idea of moral relativism is not one that can be argued for or against in an objective way. There is no scientifically acceptable proof of the idea that there is a moral law that applies to all people in all places. Neither is there any acceptable proof that different morals apply in different cultures. This is something that we must take on faith. Therefore, a true moral relativist can answer any moral dilemma. It is always possible to simply say that a certain practice is moral because a given culture says it is.
Let us illustrate this with perhaps the most extreme possible scenario. We might think that there is no way to justify the killing of children for something like religious purposes (sacrifice) or political purposes (like using children as soldiers). This, then, would be the sort of specific moral question that this question asks for. We could argue that it can never be morally correct to kill children.
The problem with this is that there is no proof that it is not moral to kill children. In the examples given, we can at least argue that the death of the children serves a greater good. By being sacrificed, the children help to propitiate the gods and, thereby, allow the community as a whole to prosper. By acting as soldiers, the children help to bring a specific group (which obviously thinks its rule is best for the community) to power. Thus, they are laying down their lives for the greater good. There is no way to prove that it is wrong to ask (or force) children to do this.
There are clearly examples, such as this one, that we could not possibly condone in our society. And it may be that we are correct. However, we cannot know this objectively.