I have a couple of fee arrangements.

A) full time is paid for monthly and in advance. I will also accept payment twice a month by dividing the monthly fee in half. But still paid in advance!

B) part time, guaranteed. I charge a slightly higher daily amount for p/t than what it works out to for full timers. This is because they are taking up a spot, and yes, it can be irritating to have rotating/changing schedules. For example: a family knows they need at least 6 days of care every month. 6 x my daily p/t rate= what they pay me, in advance, monthly. Should they require extra days, they just pay the daily fee that day. Should they require less days, too bad. This way they are guaranteed care when they need, and I am guaranteed a specific amount, sometimes more. Let me tell ya, they almost always use all 6 days. Even if they don't "need" them. But I don't begrudge that.
I normally keep one "space" for this type of arrangement, but would not do this if I needed all f/t placement.

C) part time, drop-in, is subject to availability. I ask for 24 hrs notice, and reserve the right to refuse if I can not accomodate. The daily payment is expected by the end of that day, or you will not be welcome back.

I also don't know why one family would be mad, since they DO NOT need to know what others are paying. It's not any of their business, frankly. It's YOURS! Why is it unfair? P/T care is pretty much universally more expensive on a daily rate than full time care. Due to all the reasons I listed above, and more!!