Truth or Dare
Parents of 2 home children feel stuck sometimes when their child starts a sentence with "but at Mommy's house...." or "but at Daddy's house...." Parents know that sometimes it is manipulation because the child doesn't like the answer they are getting! And they also know, or at least strongly suspect, that the child at times is making something up on the spot to either get out of trouble, or distract a parent from an action the child doesn't like. When a parent knows the child is telling the truth and knows the rules are just different in the two homes, it is pretty easy to deal with. But when a parent knows that what is being reported is probably not true, they wonder how to handle it. One effective way to proceed is to check it out with the other parent, but not immediately! That may be just the distraction your child is hoping for. The best thing in the heat of the moment is to stay focused on the child and continue down the path you were on. File it away for later as something to discuss with your co-parent.
So let's say you stick to your guns and keep the focus on the issue at hand and you get the kids to bed. Once they are down for the night, and you get a cup of tea, you sit down at the computer and email your co-parent. The response you get back makes it clear that either your child fabricated a tall tale or your co-parent has. In this situation, you probably want to give your co-parent the benefit of the doubt. The moral development of children can be a great mystery in just about any family situation, but the issue of honesty tends to be a particular challenge for children living between 2 homes.
This developmental issue in and of itself makes a good case for the critical importance of a good-enough co-parenting relationship between the parents/important adults responsible for 2 home kids. The more estranged the adults, the more likely it is that children will use that communication gap to manipulate the truth and their way out of uncomfortable situations in both homes. Parents sometimes contribute to or even cause the problem by being dishonest themselves about why they don't speak to the other parent. If you are a model of blame and rationalization when it comes to your co-parenting relationship, then you have set the tone for your children, and not in a helpful way.
Truth-telling takes courage, sometimes a lot of it. Most 2 home kids have seen eye-rolling, grimaces, and smirks when talking about the absent parent in the other parent's home. Or they may have heard sighs, grunts, and inappropriate adult communications about that parent. This leads them, too often, to feel like they need to hide any positive feelings they have for a parent when in the others' home. It will definitely have a negative impact on their self-esteem and their ability to trust the people closest to them. And it will shape the way they think about truth and honesty in relationships.
While children need and deserve to be protected from all the gory details of the divorce/separation/adult relationship, they also need and deserve honesty when it comes to both parent's acknowledgment of their own deficits in being an effective co-parent and doing so without the defenses of blame and rationalization. If you make a mistake, admit it and apologize or ask for forgiveness. Then work at doing better, don't just give lip service. An honest effort to do a better job at co-parenting goes a long way with 2 home kids working at learning how to go back and forth between 2 parents they love very much.