I'm very surprised that they were rude about this. I'm not surprised that they would not treat you while you were holding the baby. Breastfeeding should not have been the issue here. Most dentists will not perform dental work while you are caring for a baby or a child. To do so may put the baby in danger. Liability is the big concern in our modern world.
Also having you care for your baby will distract the dentist. Not because you are breast feeding but because you are focused on something different than getting treatment. Because you are holding the baby or even if the baby is in a car seat in the room it is likely in a 2 hour session that you will need to respond to the baby which would then interfere with the work being done.
My grandchildren's dentist requires that the child not being treated not be in the treatment room even tho their appointments follow each other. So, at first I would go and wait with the one child while their mother went in with the other. Now that the children are older the one child goes in by himself and I wait with the other in the waiting room.
I would call the insurance company. They may be able to get you in with a different dentist. I'm confused about why their plan has only one dentist. I would focus on their rude manner of handling the situation instead of the breast feeding issue. As you know breast feeding is an emotional one for many people.
I would also find out who owns the dental practice and write that person a letter of complaint. If it's a one dentist office it may be that your dentist is the owner. I sounds like you never talked with him at the time.
I would not call the office and make demands or threats. That is stooping to their level. Deal with this in a classy way.
I am surprise that the attorney told you to apologize etc. Is this an attorney who specializes in civil rights and/or women's issues? If not talk with one who has had experience in this field. You may have grounds for a law suit.
If the attorney made that recommendation because you wanted to get earlier treatment his recommendation is correct. I know of no other way you can get an earlier appointment. Apologizing would not effect future legal action. It might get you in to take care of your teeth/tooth.
I understand why you would be upset and end up crying. It sounds like they were not sensitive to your needs. At the same time it's possible that you made the assumption that they were refusing to allow you to breastfeed when their intent was to have you find someone to care for your baby while you received treatment.
It is best anytime you have needs different than the needs of the average patient to call in advance to make arrangements.
I had a similar experience with the police. I am a retired police officer. The police were called to my cousin's house and I assumed that the officer was not hearing me when it turned out he wanted to talk about something different than I thought he was asking about. He and I exchanged heated words until I stopped talking long enough to actually hear him. Sometimes, especially when we've had similar experiences or heard of similar experiences, we jump to conclusions when we should first listen.
I understand why you are feeling embarrassed but you don't need to be embarrassed. Tell yourself that you did the best that you could; that you were standing up for your beliefs, that they did not understand you and as a result you were involved in miscommunication. Communication is difficult. So let go of your anger and your embarrassment and focus on finding a way to get your dental needs taken care of. Your need for treatment far outweighs your need to prove a point.
We all have to compromise at times to get our needs met. It may be illegal to send you away based on you breastfeeding tho I'm sure that if you do take them to court they will say it was a safety issue unrelated to breast feeding. Consider that you dealt with a couple of people who have poor people skills and let it go at that. What do you gain by continuing the fight? You will be unable to change those people. You are making yourself miserable by insisting that you win.
Here is a note about apologies. My mother taught me that I could apologize without admitting any wrong doing just by saying, "I'm sorry that (this incident) happened." YOu could say, I'm sorry that we had this misunderstanding. As you know the Dr. has begun treatment and I really do need more treatment so that I'll have less pain. Is there any way that he could see me this month? Perhaps I could come in for a couple of shorter appointments. My mother will watch my baby." You would not be admitting any wrong doing. You would be reasonably complying with their "rules" and you would get your teeth fixed. Everyone is a winner.
A thought: I'm not sure that it is illegal for a private office to refuse to allow breast feeding in their waiting room. You are on private property and not an employee. I think a dental office would be different than a store open to the public. You might look this up on the Internet. The legal question becomes is the dentist office a private or a public place?