Copper and Easter Week
Did want to note that the week ending in Easter Weekend was HUGE in Copper -- lot of fun, but, yes, to be truthful, lot of people; it was as busy as around Christmas time!
That said, I do think Copper is GREAT for families, since the terrain is naturally divided more than just about anyplace else I can name.
Also, for lodging, if your kids like water and pools, check out The Cirque. It is a WONDERFUL family-friendly resort. It features year-round(!) outdoor pools -- a wading pool and a bigger, decent sized swimming pool, as well as what might well be the largest hot tub at all of Copper.
Full disclosure: yes, I'm an owner there. I have kids, who are water, as well as snow, kids, and I'm local (Boulder area,) so it was just WAY too good a deal to pass up!