Can there be objective morality with a God? If God is the source of morality, then morality is subject to the will of God, so isn't it by definition subjective?
There can only be objective moral values with God.
When we state that objective moral values exist, what we mean is that there are moral values that govern all humans, regardless of whether or not those humans want those values to govern them, like those values, or accept those values.
If moral values were the result of popular vote, then they would only govern humans because humans had decided to allow them to govern them. Then moral values would not be objective, but rather, subjective.
However, moral values are not subjective in this sense, in the sense that they are the complete invention of the minds of those they govern. If they were subjective in this sense, Hitler's Germany would be no less moral than any other society, and this is not the case.
Thus, moral values are not subjective in this sense. Instead, they are objective in the sense that they govern all humans, at all times, regardless of those individuals' approvals.
If God did not exist, there would not only be no concept of "ought", there would also be no one around to conceptualize it.
Since there is a God, there is a Higher Moral Authority, and therefore there are things we "ought" to do. One of the first and foremost of these things is that we ought to obey our God.
Thus, moral values that govern humans stem from the existence of, and perfect qualities of, our Creator, who is an eternally objective reality. They do not come from the whimsical fancies of a transient consciousness.
So, no, moral values are certainly not subjective.
What evidence would convince you that your worldview is incorrect?
If God is a mysterious unexplainable trinity, then why, when Jesus was posed the question which of the commandments are greatest, did he reply "Hear O Israel The Lord OUR God is ONE?" Note he's not preaching the trinity.
Do you "earn your way" to heaven in Islam?
If God said "Thou shalt not kill" then why did he flood the whole world leaving only Noah and his family alive, and how is the destruction of Sodom justified (killing people for engaging in "immoral" sex), is God exempted from morality?
Who is the Last Imam? When is he to come? Is this in the Qur'an? Where does this belief come from?