These people who are working with your daughter are NOT acting professionally. They are putting the blame on you to keep from getting in trouble. Do not be cowled by this. The therapist has no business raising her voice. Speech is hard work and sometimes kids don't want to do their lesson and you have to come down hard on them to nip that in the bud, but there's a big difference in YOU doing it and the speech therapist doing it. For example... my son's speech therapy (which was not at my home) was twice a week, and I did his home program FAITHFULLY twice a day. One day he got his back up and refused to work with the therapist. She told me that she wouldn't bill me for that session, but she would have to if he did it again. I took him home and put him in his room and told him that since he didn't work with his speech teacher, that he had to stay in his room by himself. I brought him a boring sandwich and let him come out only to go to the bathroom, and before too long, he was begging to come out. I told him AGAIN point blank why he was in there and why he would stay in there. Then he was begging to go back to speech. I told him that the teacher was with another child who appreciated learning how to talk better and we couldn't go back until Friday. I kept him in that room as long as I had decided, which was several hours. Tough, yes. But he learned his lesson the HARD way and never did that again.
If his therapist had raised her voice at him, number one, it wouldn't have worked. Number two, I would have complained to high heaven.
You need to get yourself together and call that chairperson back and tell her that you expect her to listen to your concerns and and not just to these people who are not acting professionally. Being late, leaving early, raising voices at your daughter which will NOT help, is not about "not making you happy." It's about short-changing their client that they get paid to work with. You also need to find out who the chairperson's superior is and how to contact him or her before you talk to the chairperson. If the conversation doesn't go well, write a letter to her reiterating what is happening and that you want a change of therapists, and cc it to her superior. Tell her in the letter that you are writing because you don't feel that your concerns are being taken seriously. THAT should get her attention, and copying it to her boss will make her get this handled. Either you will have different therapists, OR they will stop their unprofessionalism.
If it gets to the point that you have to write that letter, ask a friend to proofread it to make sure it says what you mean to say, sounds professional, and has good grammar and spelling. Don't say that they treat you like scum. Don't make it about YOU. Make it about your daughter and treating her in a professional manner. Being late, leaving early and raising voices is NOT professional and shouldn't be tolerated by their superiors and your child deserves better.
Stop crying now and make yourself stand up for your daughter and feel strong about it. AND when the therapist isn't there, work hard with your daughter in her home program and show her point blank that she MUST work without fussing with the therapists.
Good luck!