I think that school is only one of the places where children learn about kindness and acceptance , but the first place should be home. You are guessing and assuming that the mother is not teaching this lesson but you know with certainty that your partner is not teaching this lesson.
Given that the older sibling does not respond in this fashion, it may or may not be something that his mother is specifically saying. However, if she has associated her pain and his father's leaving with you. The child may easily have associated pain and negativity as being caused by people of colour.
It is your partner's obligation and responsibility to be proactive in teaching his children about politeness, kindness, acceptance, or even just tolerance of others.
This child has 2 parents , one of whom is clearly conveying her hurt and pain to the child and the other is standing on the sidelines and criticizing. Neither is being a good parent.
You can buy books on diversity. There are some very good children's books on the topic. However, in your place , I would find his father's failure to act as or perhaps more off putting than the mother's behavior.
I would find your partner's failure as a father and cluelessness as a partner traits ones that would not inspire me to have much respect for him.