There is no reason one cannot limit the Internet to two days/evenings a week or any variation thereof, just as many families today regulate telephone use during meals or certain events. I have family-friends who have a 24-hour period every week that is for them alone. There is also no reason why one cannot set an evening or three or five as 'game nights'. This is rarely an all or nothing world. Making hard and fast rules like that, to me, is too much like forced nostalgia.
That said, I hope the both of you enjoy your new lifestyle.