You could have handled it better. If it makes you uncomfortable, you should have said something reasonably soon after she started. And you could have done it nicer. Remember, this is your FH's mom. You would be mad if he yelled at your mom and told her she was being disrespectful, Right?????
The better way to handle it would have been to just say that you are uncomfortable with the "new mom" phrase and would prefer to just call her by her first name. Explain that in your family, the in-laws are not referred to as "Mom" or "dad", but by their first names and that it is just something you are not used to. You could have pointed out that maybe your mom already feels as if her "baby" is growing up and she is "loosing you" (even if your mom doesn't feel that way) but that you don't want your mom to feel like she is being replaced either by you calling someone else "new mom", even if it is your FH's mom.
While she may have been rude in your eyes, she was actually just saying in a round about way that she is excited to welcome you to the family and happy that her son chose you. It was a compliment that she thinks you are good enough for her son and WANTS you to call her MOM. Even though you feel she was disrespectful, you were 10x more disrespectful by telling her off like that and telling her straight up that you would never even think of her like that.
Hate to say it, but when you marry your husband, you are also marrying into his family. It is no longer "Your family" or "my family", but OUR FAMILY. I call my husband's mom "Mom" and it is because she is my mom. Not like my own mother, but she is the one that raised my wonderful husband and was/is there for him. And in turn, she is also there for me. When he is deployed, she calls to make sure I am ok. She was part of planning my wedding. She is part of my life. While she will never replace my real mom, she is a big part of my life....and a big part of my husband's life.
At the very least, haven't you ever been taught to respect your elders? If you couldn't have handled this in a polite, grown up manor, you should have had your FH talk to his mom for you. He would have known how to explain it to where it wouldn't hurt her or tick her off.