What's the Genre?
The genre of the text is key to understanding its intended meaning, which is the goal of biblical hermeneutics. This is a dream, not a prophecy per se (e.g. 'Thus saith the Lord') - and this dream may be given to communicate a general message, not to forecast an exact outcome. It's not obvious from the text alone that we should interpret this personal dream using context from a distant section of the text, so let's try reading locally:
A. Interpretation as a dream
Joseph's dream was intended to communicate to him in the immediate context of the passage, in Joseph's here-and-now. When this dream occurred, he had a father and mother and eleven brothers, and so there was a perfect correlation and an interpretation so plain that even his brothers understood it properly. Any variance in that number would have produced an unclear dream and would have made for messy interpretations. It wasn't intended to be re-interpreted long afterwards, but rather to make sense to Joseph and his family at the time when it was given.
B. Interpretation as a prophecy
We can assume it as prophecy if that is the genre you feel the passage belongs in, but even then we can take the same line - the "fullness" of his current family bowed down to him in the dream, and then the "fullness" of them came to seek him in Egypt for refuge, symbolically bowing before him for food and safety, even if they did not all have to literally prostrate themselves.
Are there any contextual clues?
Thankfully we are not just given the one dream, but two, and these dreams are given and interpreted side by side. Just before the passage in question we have Genesis 37:5-8:
Now Joseph had a dream, and when he told it to his brothers they
hated him even more. 6 He said to them, “Hear this dream that I have
dreamed: Behold, we were binding sheaves in the field, and behold,
my sheaf arose and stood upright. And behold, your sheaves gathered
around it and bowed down to my sheaf.” His brothers said to him,
“Are you indeed to reign over us? Or are you indeed to rule over us?”
So they hated him even more for his dreams and for his words.
This 'first dream' suggests that these were intended to show that he would reign over his brothers, and this is how his brothers naturally interpret the bowing of the sheaves. If we use a consistent hermeneutic in the second dream, we don't require all of his brothers to literally bow to him.
Similarly to how there is one brother from the dream that does not literally bow to him later in the text, it should not trouble us that we do not see both of his physical parents literally bowing to him either. This lends support to the stars of the second passage being all of his brothers, and therefore the sun and moon are his parents.
Using a consistent hermeneutic which considers the local context and genre of the passage, the Sun and the Moon refer to Jacob and Rachel, Joseph's parents, as per Jacob's own interpretation in Genesis 37:10: "Shall I and your mother and your brothers indeed come to bow ourselves to the ground before you?”. This is the most natural reading of the passage, and though it doesn't see a literal prophetic fulfilment in all senses, the wider sense of the dream is definitely fulfilled and doesn't suggest that the given meaning of the dream was incorrect.