There are so many things wrong about this and your concerns are very well-founded. While there are no laws that I know of that would stop a counselor from this type of muddled therapy it certainly doesn’t allow the best and unbiased therapy for your daughter.
While there may be cause for a one-time, or perhaps occasional meeting with a family member (sometimes called caucusing) the on-going nature blurs the boundaries. It is likely to affect what that individual will share, the truth of what is revealed, and the depth. There are plenty of good counselors out there and to give your daughter the best opportunity for safety and her own growth. Having her see someone not conducting therapy with a parent is almost always a better option.
In your daughter’s situation think about the implied concern she could have in revealing information to the counselor. What if she is having an issue with the mother’s boyfriend? What if she has a concern with you? What if she is engaged in a behavior that you support, but her mother and her boyfriend do not? Each of these concerns would require the counselor to be unbiased. Even if he or she were perfectly so it is the perception your daughter would have that the counselor may carry the bias.
Finally, the fact that you are uncomfortable should be enough of a concern. While you haven’t said your daughter’s age, if she is under 18, I believe the parent’s agreement is essential. Under 18 you should have the ability to rule out the counselor if you feel there is a bias. If you are unhappy with what is going on I would voice these concerns with the therapist. It is valid and important to express. If she is over 18, her choice of a neutral therapist should be what determines who she sees.