I agree from a human perspective, but if you believe in divine command theory it must necessarily be the case that when God said it was good, it was good. And when God said it was bad, it was bad.
I don't think that is true. For morality to make any sense, there needs to be some rationality behind it. Therefore God can't get away with anything simply because he is the creator. Even if God were to decide morality it needs to make sense for him as well.
If morality, in the sense that it is created or even evolved one must be able to judge former moral standards as being either right or wrong, or said in another way they have to develop.
Like in the past when we did human sacrifices, we can now look at that and conclude that it was morally wrong, due to the development we have experienced throughout history. But God does not follow these rules as he is said to know the past, present and future. So he would logically know if something is immoral or not.
Now, this doesn't mean, as you say that morality even God's couldn't change, but it would still need to be justified. Like, God believing that homosexuality is a sin, punishable by death, to then suddenly not be. The justification that homosexuality was a sin to begin, and that this from a human perspective doesn't really seem to matter at all. And I would risk my head saying that whether a person is of a given sexuality bears no impact on whether a person is "good" or "evil", not back then and not now or in the future.
So if God were to change his mind about this, he would need to justify why it was ever considered wrong to begin with, and obviously, it would be nice if he would justify why it is even considered wrong at all.
I think nowadays openly embracing divine command theory is a bit "out of vogue", but when ultimately challenged on objective morality it's what a lot of theists seem to adopt without knowing it. I don't think that makes them bad people, or even necessarily wrong, but if you believe that God sets the moral standard and no standard can objectively be said to exist outside of God, and that God's commands must necessarily be moral, you essentially adopt divine command theory. There's nuance there, to be sure, but broadly speaking it's a "if it walks like a duck..." scenario.
The most common answer in my opinion when believers are presented with a moral question which is very difficult to answer is that
"God works in mysteries ways",
"We are not able to understand God's plan" or something along that way and translated into common language it means that they have no clue or answer to it.
Because even if you believe there is a God and that God is the source of objective morality, you still need to determine what that moral standard is yourself, and since you are not God (at least, in most cases?) you can only do so through subjective analysis.
In other words, even if you believe there is an objective moral truth, you still need to pick and choose which set of truths you THINK are the objective ones based on a set of either arbirary or subjective criteria (such as choosing to follow the Bible vs. the Qur'an, or mixing up various passages from either, or rejecting all religious texts, etc.).
I don't think so, as it would go against the meaning of objective morality.
"Killing/torturing infants are wrong" you don't need a religious scripture to have an opinion about that, in fact, I would probably argue that most people haven't even given any thought to whether it is actually wrong or not, it seems to be a given that it is. And those that are supporters of objective morality will most likely argue that it is because God wrote in our hearts or something or that it is simply part of life if one does not assign it to the divine. But at least as far as I know, most if not all lifeforms seem to not eat their own offspring.