Here is the problem I see. She is working for you as her full-time gig, even if you don't need her full-time, she can't go get another job AND work for you, especially because her schedule changes.
She cleans your house, watches your kids, AND does your and your husband's laundry and you only pay her $13/ hr?? WOW! You guys are making out BIG TIME!!
Also, I have never heard of someone not paying their nanny because THEY chose to take time off. That is INSANE. She isn't picking to be off, you are. She isn't saying "I don't want to be paid right now." You're saying "We're not using you this week and you're not getting paid." Not fair. (I know you said your friends do this, and I think that's horrible of them.)
Here is my current set up. We hired our morning sitter for $8/hr. Her schedule is supposed to be 615-845, and she drops our 4 year old off at his regular sitter. So it works out to $100 a week IF she works all 5 days and all of the hours. I pay her $100 REGARDLESS. My husband travels to different clinics and when he does that he gets to leave later, so she doesn't have to come until 7 on those days. Our choice to lessen her hours, not hers. She gets paid.
She also gets every other Friday off, I still pay her. So on any give week, she is paid $50-75 MORE than what her hourly rate gives her. We don't care. We LOVE her.
She gets our kids up at 730, gets them dressed (clothes already picked), gets them breakfast, tells them to grab their already packed lunches, grab their backpacks which are by the front door, and she takes the older two to the bus stop. The 4 year old goes about 10 minutes away to his daycare for the morning.
One thing that annoys me is that she doesn't do the dishes, or have the kids do the dishes. Dirty dishes in the sink is my biggest pet peeve ever. I still don't care.
She is FABULOUS and we will pay her until she quits us.
You are underpaying your nanny and not giving her very good benefits (time off). I think you need to reconsider what you can afford to pay her and pay her accordingly (at least $15/hr for what she does) AND give her at LEAST one full week paid off. You need to still pay her when you take off too.
I hope that isn't too mean. I was a nanny and I wouldn't have stayed in your situation (unless it worked for me too - school or something). The family I was a nanny for is a close family friend of my parents and they screwed me BIG time. I still have a chip on my shoulder from it and it ended 7 years ago. They told me they were paying me under the table and then claimed taxes on me. They told me I was paid when they took vacation, came home, and refused to pay me. I love them all to death, like family, but I still begrudge them the tricks they tried to play on me.
The last straw was when she called and asked me to watch her two boys for Christmas break at the same rate. I was ALWAYS paid $200 weekly. Never daily. They tried to pay me daily. Not my fault there were holidays. I had the nerve to tell them it was wrong and they paid me for that.
Don't take advantage of your nanny though. YOU have a great set up, her not so much. Compensate her accordingly.