He doesn’t have rights, the child has rights to see his daddy.
At one year old, unless they have a very strong bond, it’s a bit early for overnights. It would be better to build their bond some more, maybe a whole day at the weekend, and introduce the idea of staying with daddy next summer.
But if you aren’t happy, if there is something specific you are concerned about, you could let him take you to court. Will he bother with the paperwork?