I consider 4 days a week fulltime too but if you did give a discount it would be part way between what would be 4xyour daily rate and 5x your daily rate to compensate.

Since you have two families wanting a day off per week is it possible for it to be a different day. Then there is a very good chance you could find a client needing two days a week - even a mom home on mat leave looking to get their child out and about a couple days. Just make sure they realize once they have gone to 4 days they may lose the chance to ever use the fifth day meaning if they are not paying for it you do not have to be available to them ever on that day.