I don't like calling the weekly day off 'Family Day'. Mind you, I think 'Sabbath' can be a little unhelpful too.
I love spending time with my family on my day off and I think I should love it. But there is more to rest than minding your kids, giving your wife a break and walks in the park.
Sometimes I wonder if 'Family Day' implies that you are not seeing your family any other time during the week. That's a bit yucky.
Also, some guys, and I'm one of them, also need 'me time'. Is it somehow unspiritual or anti-family for those guys to want to go bush on their day off from time to time? Or build a cupboard? Or play soccer?