Some of the advice given so far isn't quite right. Whilst it's true that a self employed person can choose their own hours i.e. whether to work/make money this week or not, don't let that confuse you into thinking that you can go to the owner of the salon and say "right, I'm not working on Tuesday or Wednesday and on Saturday I am going home at 2pm" because that's not how it works either. Not if you want to keep your job/income.
Many people (especially the young) hear from a parent/uncle/friend that they can choose all of their own hours when they are self-employed and it lands them in hot water if they start going around trying to dictate to business owners their terms. When the business owner says "I don't think so, get out of here!" they're often quite shocked.
Try to think of being self employed as a stylist as being exactly the same as a mobile hairdresser, and it begins to make sense.
When you're mobile, you will offer your client a date and time that you will provide services of her liking and choice at a price you both agree to. A contract is formed there and then where your client becomes the customer and you become the service provider. Your client expects you to turn up at the right location, at the time agreed and perform the agreed services for the time allocated and for the price you mutually agreed. You can't just call the client and demand she lets you into her house at 2AM to perform the services, or expect her to allow you to visit her on Tuesday when she is only available on a Thursday. If she is requesting you to do the service on Thursday at 3pm you have a choice as to whether you will take the appointment or not. That's what is meant by being able to "choose your own hours" when you are self employed. Once you have accepted the appointment and confirmed it with your client, you are then obliged to 'fulfil the contract' i.e. turn up and do her hair.
It is no different with a salon owner who rents space/splits commission etc. In effect, s/he becomes "your client". They are asking for an appointment every week from 9AM-5PM Mon-Fri. You agree a price and terms of contract and you are set to go. Just like a mobile client, if you mess them about by changing the agreed times or prices, they will look elsewhere for someone more reliable or able to do the job. You both have choices, in the same way you have a choice when you advertise for a builder to come build your new extension - you would tell him the price you are willing to pay, he would tell you how long it would take to do the job, he would tell you which times the crew would be turning up each morning and which days they wouldn't be working. See what I mean?
Just thought I would clear that bit up in-case you get confused.
The 12 hours booked solid though is your personal choice. If you don't mind working this way and can squeeze in some lunch while one of your colour clients are developing, then it's up to you. Make hay while the sun shines.
However, if it's more a case of the salon owner has just done a groupon or something and is filling up your appointments without any consultation to yourselves, I would nip it in the bud immediately and let them know that part of you working with them means being able to eat at lunchtime and take a quick break throughout the day when you need one. Tell her that as her salon is so busy at the moment, you will need to mark out a half hour lunch in the appointment schedule to guarantee you get time to eat.
If she refuses this basic request, come back and let us know. Otherwise, good luck!