I think you need to realise regardless of how you feel, you are an employer and as such need to act within the best interests of the business. I would sit her down and say to her this is the situation, due to business needs she is no longer required. You need to think of yourself, your business, your image, your reputation, your cash flow etc etc etc.
Alternatively you could take the nice route - Ask her if she enjoys the job and if so, what does she enjoy about it. What does she hate about it. Get her chatting. Once you hear her side, you may find she is best suited to working as a Saturday girl with you or perhaps she's just not confident enough to win back clients and take on extra hours and you will get to the route of the problem. I would be harsh if taking this option though and give her 7-14 days to either turn it around and take on extra hours (contracted) or she may no longer have a position.
Please don't worry about what clients think of you in terms of hiring and firing. Clients are happy to know you are giving them the best and if someone new appears and you really sell them, clients will be pleased with that. I think before speaking to your part timer it may be worth speaking to the therapist you would like to bring on board and just see if she would be interested IF you had a position to offer her. She may be happy with part time work so you could have both or she may have something else in the pipeline.
Just a suggestion as you may be doing this already but I don't think you are, I give all employees a 3 month probationary period and during this time, either side is required to give 7-14 days notice should they leave depending on the area they work in. This gives you the option to sit down after the 3 months and let them know if need be that it's not working out and best to go separate ways. This completely covers you. You can get employment contract templates for free on line to re-jig as you want to. Sorry I can't find any links to post but it just ensures you are totally covered.
It's never nice to let someone go but you just need to remind yourself of all the reasons why they aren't suitable and it will be easier. As long as you have evidence of poor performance, you're clear, concise and diplomatic then they have very little comeback :hug:
Good luck x