The courts do not necessarily look badly on living together any longer even if there are no marriage plans. The fact that you are engaged will help.
Seeking more visitation with your child is usually a good thing that the courts like to see. They want both parents involved in the child’s life as much as possible and unless there are legal implications about who the parent is living with, such as criminal history, drug/alcolhol use, physical abuse history, they do not generally base their decision on who the parent chooses to live with.
If you are planning to marry this person, I suggest that you have them come to court also, if they are an upstanding person who wants to have a relationship with your child, it will look good to the court that they are there and willing to be questioned about their background, ethics and motivation. It may not even come up, but if this person is going to be your spouse, and the child’s stepparent, they are going to have more involvement in that child’s life. The courts may want to know more.
If you are not divorced yet, the courts may have more of an issue with the situation of custody visitation. But living with someone without being married is no longer illegal in NC, so that part of it should not matter if you are divorced.