K.F.
What their mother told them was wrong but by the same token you may have helped add to the confusion by correcting their mother's stance. Instead it may have been more beneficial to ask the children about how they felt and what they thought over bringing your thoughts into it.
I'm a mom and a step mom. I often find myself correcting the children and getting them to maintain their respect and love for the parent they don't live with. Even when I don't agree with the methods used by that parent, that parent still needs to be respected. You don't mention how old the children are but as they get older they will try to create a divided front between the adults so they can have their own way. All the adults as much as they can need to try to be on the same page
Even their mother is entilted to a difference of opinion regarding how many homes they have but try to not put the children in the middle on your side. I hope this helps.