It depends on the intention of the wife, if she hopes to convince her husband to return then it is not considered as abandoning the homeland and if there is no hope, then it is considered to be an inevitable abandonment.
If a person wants to stay 10 days or more in a place, in this case prayers should be performed complete and the person must fast. And if this person wants to stay less than 10 days then prayers should be performed shortened and the person cannot fast. The beginning of 10 days is from the moment of entering the destination, for example from noon of the first day of arrival until noon of the next day is considered as one day.
The Paternal homeland of a person is not considered as the homeland of that person unless he/she stays there continuously for a long time like one year.
Your prayers and fasting should be performed complete in both places.