I think your greyhound is getting jealous and just warning the newcomer that DAD IS HERS! Same thing when you came home from work, I think she is just protective and wants all attention from you. I think it went well the first day because they thought it was just another visit... but when the pup didn't go home and stuck around, they're starting to think a new pup has moved in!!

You need to keep them separated as long as aggression exists and introduce them graudally more and more throughout the week. Do not leave them alone together unsupervised.

You just need to give your greyhound a little extra attenion, the poor girl probably thinks she's being replaced!! Who is the first dog you or your husband greeted when coming home from work?? Greet the greyhound and your corgi first, and your parent in law's pup last.