I have come across this a couple of times, most recently when trying to book an appointment with someone to use a voucher I was given (ie that they've already been paid for). My daughter also has a friend who is never ever available for a playdate at a weekend because they it;s family time.
So, people who can't do anything at a weekend because "family time is sacred"??? I have three kids, we are very busy, family time is very limited, but we fit in our 'quality time' when we can, in between the million and one things we have to or want to do. I wouldn't dream of refusing to do something at a weekend just because it's a weekend and all the family are at home (If we actually had something specific planned then that would be different). We are ludicrously busy during the week after school so weekends are the only time we can fit anything in.
So my question is, if you have the policy that weekend family time is not to be interrupted by anything, do you really spend the whole weekend engaged in 'quality time' social family activities? Do your kids not ever watch crap kids TV or films while you get on with something, or just play in their rooms, read etc?
In both the examples I've come across I'm not asking someone to spend the whole day doing something, it would be less than an hour out of their day. I'm just not sure why it would be so dreadful for the child to entertain themselves (or be looked after by the father) for 45 minutes while the mother does something, or for the child to go and see a friend while the rest of the family get on with other things.