Is there any remedy for this or will it pass? Do I have to buy another dog?

What remedy are you looking for? resurrection?
Dead is dead.
I presume you bought your dog either from Castle Sunguard or Markarth, if you want another just go buy one.
Or find a stray, i do not understand your problem.

The kids will get over it eventually, but I doubt you will be able to get another dog, or a replacement pet. The only remedy would be to load a save game before the child adopted the dog, or before you killed the dog.

it takes 24 hours for the kids to get over there pet death.

It took like 1 in game month for me to get Lucia to re-adopt after her bunny died.I did use console commands and player moveto. .not thatt this worked.I placed pincer (who now lives at my front porch)right infront of Lucia and she just totally ignored it.Thhough tey very next day she did ask to adopt Vix.

Teach 'em some conjuration...then they can get their dog back.