When you're self employed, it's up to you to negotiate the best terms for your business. However, in contrast to being employed, there are few rights or laws to protect you. You can't think in terms of employment rights.
You are a fellow business owner, not a member of staff.
HMRC drafted the guidelines to discourage salon owners from blurring the lines between employed/self employed. There are salon owners that treat their chair renters as staff by keeping client records, issuing rules, uniforms, setting prices, taking bookings via the salon phone but not paying tax, national insurance, holiday and sick pay etc.
HMRC will prosecute a salon owner if they believe that the salon owner is acting improperly. They can fine them as well as requiring them to pay back the tax, NI contributions and calculate the minimum wage the self employed person should have received. Being investigated by HMRC can be very stressful.
As a self employed chair renter, you must negotiate your terms directly with the salon owner. The daily rate payable is part of the terms of the contract between you and the salon owner. The salon owner could reasonably suggest that the daily rate is for a 9 hour day but as you've been working longer days for a while, it's up to you to argue that your understanding from the outset was that you set your own working hours for each day. If she had issued a written contract at the beginning that stated rent payable was for a 9 hour day and you had agreed to it, that would be the end of the matter.
Her mistake was not issuing a detailed written contract.
Many owners don't bother because they don't want to spend money on solicitors fees but then they get into a grey area and try to insist on a particular rule but you don't have to agree. It's up to you to negotiate what's best for your business. She can always increase your rent to compensate for her lost revenue but equally, if you're not working on say Mondays, she can rent the chair to someone else that day. Bear in mind that if you're on your own in the salon over several evenings, she's having to cover extra heating and electricity costs that she might not have initially budgeted for.
However, if it suits you to work there, try to find a way forward to satisfy you both. Would you be willing to pay a slightly higher daily rental fee? If she's not willing to compromise, you or she can agree to part ways.
By referring to the HMRC guidelines, you can use them to help you negotiate a reasonable deal and not be treated as a second rate employee. However, they are just guidelines so use them as part of your negotiating tactics. You want to work in a salon where you feel comfortable and not ill at ease.