How is it appropriate to be involved with your ex’s family after the divorce?

Your kids need to understand that divorce ends a marriage but not a family. The family members whom they enjoyed for many years at holiday gatherings and family reunions should still remain part of their lives and both of yours, even as the family has reconstituted itself after the end of the marriage. I would hope that your ex-in-laws would feel the same way I do about retaining those familial ties. If a loved one from your ex's side of the family gets married, has a grandchild, or passes away, I think it's entirely appropriate (within the context of how nice or how toxic your divorce has been, of course) for you to acknowledge those events with your presence. It will show your children that you value the time you spent married to their other parent enough to continue to respect that family's members.