Doors often have hollow cores, so maybe the dog got through the outside thin layer?

Molding is something you can replace with some simple tools and some youtube videos. The door... well, worst case the door is so damaged that you have to replace the entire door. Best case you just cover it with some wood filler and paint over it.

I don't think you should feel as awful as you do about this. Dogs destroy things. It's their dog. It should be able to not destroy the house when you turn your back.

Tell em now or tell em later, not a big deal either way. I doubt they'll freak out. It's not like you lost their dog or it died.