My Ex partner has decided that he wants to see our daughter on specific days of the year(xmas day etc). He already has her for one night and the following day. He has never been able (his choice due to working)to have her during holidays and has never had her for more than one night. She is seven. He now keeps threatening me with court if I don't agree with his demands. What can I do?

Call his bluff. You need a custody, visitation, and support decree isssued by the court anyway. An informal agreement, not ratified by the court such as I assume you have, is nothing but smoke and mist.

You left out a very important piece of info. Is there court ordered visitation now?

If there is, then he will need good reason to ask the court to change it. If there isn't, you SHOULD go to court to formalize the visitation schedule.