I am a salon owner in the state of Wyoming. The stylist in my salon are all month to month booth rent with no contract.
My problem is, I have one stylist that is a problem and is affecting the moral of the entire salon. I have had numerous conversations with her about her behavior which were to no avail. If anything she just became more belligerent and disrespectful afterwards.
I would like to ask her to leave, we have no contract, so do I have to give her 30 days notice? I know from past experience with her, she will not conduct herself in a professional mater and just out of spite will remain in the salon the entre 30 days.

Why would you do business without a contract? Since this is a commercial lease, landlord/tenant rules do not apply. Since there is no contract, I don't believe there is law require you to give any notice. That is something that would have been written into a contract. I strongly suggest you contact a local attorney to see if there are any laws that require you to give notice. At the same time, have the attorney draw up a standard contract and have your other "tenants" sign one.

I would, have done a contract and treat them as independent 1099 employees, where you can more easily remove them. If there is documented problems, you need to notify them in writing, of those problems, and demand that they correct such actions.

You seriously need contracts to protect your business. Please consult a local attorney.