Rights of Primary Residential Parent

My husband has 2 children from his previous marriage aged 10 and 8. In his parenting plan it states that they have joint custody of the kids and the mother will be primary residential parent. It goes on to say “she is listed as such only because state and federal laws require one parent be named.” We’d like to know what exactly this wording means. The kids want to come live with us………there’s many situations at their mom’s house, but we’d like to avoid a court battle if at all possible. She’s already told them no.