As @Letsnotargue has said, you need to start on neutral territory, going for a walk together is a good start. No matter which house you are in, one of the dogs is on home ground - when the GS comes to your home they are on the back foot - the behaviour your describe is basic dog behaviour for go away and leave me alone, unfortunately the Italian Greyhound is not reading the signals, especially at it is their home.
I would walk them together with at least two people, do not praise or be negative with either dog when they are together on the walk, almost ignore them, as it doesn't matter what you say they will see that a behaviour being praised UNLESS they are very good with each other, even for a nano second of a time, then you can praise.
In the house, neither dog is big so you could use play pens to keep the dogs apart but see each other, size wise it is unlikely they will jump over them. Just make sure they are not flimsy and may fall on either dog especially the GS, if it has been confined for its earlier life.
Over time they will tolerate each other but it is not going to happen in time for the week they will be together so walk them together and allow them their own space when in a house (if you are in the home of the GS, then the IG would be in the puppy pen). You may fins especially with the GS if it has somewhere safe away from the IG but knows it is there, it may be enough to get through the week.
My concern would be, is your husband going to be watching the two dogs enough to ensure there are no problems?
The poster who said let them sort it out, there is some truth in it, eventually dogs will sort it out but not allowing them to fight.