One day a week doesn't sound unreasonable to me, but it is her duty, when she is with you and your child, to be there fully for you. It sounds like she needs to manage her NRE better.
Also, a honeymoon period immediately prior to and after the wedding is not unreasonable. While specific time periods would be up to you and your partner, a week before and a week after might work.
The problem is that your poly experience started for the wrong reasons and it sounds like she is not living up to her obligations to her family.
Perhaps you can concede the one day a week while asking her to be more mindful of you and the little one when she is there. As the hinge in the V relationship, she has a lot of responsibility, and it sounds like she is not living up to her end of the bargain.