It would be hard to give you an honest opinion of how she is training only because I have not seen her training methods for myself. I personally believe that a horse needs one or two days off a week and it would also depend on the age of the horse and how physically in shape they are. Mental stability of the horse would be another huge part of the equation. Another factor would be how long the training sessions last. A great trainer will think of all these things when putting together a training program for each individual horse.
You need to remember above all else that it is your barn and your rules. It doesn't matter who it is, they still need to follow the guidelines you have set up for the care of the horses at your barn.
What concerns me the most!
What concerns me more is her lack of respect for you as the barn owner and how she talked to you. I have been exactly where you are in the beginning of our business and I will never go there again. Any trainer that works out of your barn needs to be respectful to you even if she doesn't like a particular question you are asking. If a trainer would talk with me now like that I would have a serious discussion with them and if they continued they would not be working out of my barn anymore. That kind of disrespect will spread like a cancer and if she is talking to you like that, it will most likely spread to her clients who many of them will also be your boarders. You might want to look at your barn rules and boarding contract and make some modifications as it relates to the horses at your barn and trainers that work there. Remember that you are the boss of your establishment and you call the shots, not her. It tells me a lot about her poor character just by how she talked to you.
One more thought - Be prepared because once you have a heart to heart with this trainer, there is a chance she might become angry or leave. I personally believe any business will be much better without the negativity and you will need to decide when you have had enough. I have been there and you are not alone. I have asked a trainer to leave and it was definitely for the betterment of the barn. We survived and the barn atmosphere became so much nicer and the business became stronger. I also became stronger as a business woman and so will you.
If you want to learn more about how to handle these kinds of situations that you will find yourself in, please check out my newest book, "The Total Horse Barn Management Makeover." It will change how you look at yourself as a barn owner and manager. You will read chapter after chapter about the dynamics of the equine professional/client relationship and how to find solutions to the issues that happen to all of us.
Thanks for the great question and I wish you the best,