My partner's ex-wife, who is also the mother of his child, has a close bond with his family and is involved in a majority of things. What should I do about this?

First, you need to understand that she is the mother of his child and the mother of his family’s grandchild/niece/nephew, etc. That is the role she plays in that family, and if the family accepts her as part of family functions, you will have to come to terms with that. She is there for the child. Talk with your partner about what makes you feel uncomfortable. Are you afraid your partner will go back to her? Are you afraid your partner’s family does not accept you? Address the issues that originate within you first and talk with a therapist if needed. Then, work with your partner to find ways to ease your discomfort. For example, do you feel uncomfortable at events when he leaves you alone and goes off and does something else? If so, see if you can work it out where he is with you for the whole event. Do you feel awkward when his family is talking with the mother? Find ways to avoid watching the interactions. Do you feel like his family doesn’t like you? Figure out ways for them to get to know you. The important part of this is separating the ex from your partner in your mind. She used to be wife and mother. Now she is only mother.