Answer

I don’t know what is meant by “values that exist in reality.” A person chooses between values. If you hold ethical realism—I’m with you. But that isn’t essential to the discussion here.
First, who says that God really chooses? Rabbi Moshe Chaim Luzzatto writes that it is the nature of the good to do good, which implies that He has no choice. 
Second, I didn’t understand why you brought “influences” into this. A person is indeed subject to influences, but choice is not the result of those influences. God is not subject to influences, but there is no reason He could not choose.
Perhaps what you mean is not that the values influence Him, but that values prior to the choice are required in order for there to be a choice at all (the choice is between them).
And even if He chooses, and even if your intention was that the values need to precede the choice, it still isn’t so simple. Seemingly this takes us into the Euthyphro dilemma: are values good because God commanded them, or did God command them because they are good? According to the second side, they really do precede Him. According to the first side, He chose them arbitrarily.
But in my opinion this dilemma is based on a mistake. He created the world, and once this is the world, the good is defined from within it and within it in a univocal way. But He could have created a different world, and then perhaps the good would have been defined differently. According to this, He chose to create such a world, and consequently those values. Here the choice is, of course, between forests of values—He chooses between worlds and different systems of values.