I like the way you handled it. Her comment was rude and therefore doesn't need a response. She wasn't giving advice. She was telling you that she didn't approve of what you were doing. Advice would be giving you another suggestion so that you could meet your goal.
I have some friends that have never had children and they also make this sort of negative comment. I usually just ignore them or look at them with a puzzled look on my face while I continue to do what I was doing that was working. I don't allow any further comments in front of my grandchildren. This means I don't make a comment. Fortunately my friends know that when I respond in this manner it's not open for discussion.
Sometimes they will say something to me later. One friend likes to tell me that I'm spoiling my granddaughter. I keep it light. I might say, well, "it's my job as the grandmother to do just that." She also says that I'm not consitently enforcing the rules with my grandchild. I agree with her because what she's said is correct. I know that I'm weak in the rules and discipline area. And I've decided that although I continue to work on being more consistent I feel OK about what I'm doing. Incidentally my friend has never had children or even been around children since she was a child. I believe that some of her criticisms are prompted by her jealousy. We've been friends for 30 years. When our friendship began neither of us had children.
At least my friend is specific about her complaints and we are able to talk about them from time to time. She never makes a comment in front of the children.
If you don't see this aunt very often I'd just let it go. If you will be seeing her often, take her aside when things are going well and tell her that you are aware that she would parent differently; that you are comfortable with the way you are parenting but if she feels strongly and wants to make a comment to me she should do it outside the hearing of children.
You did handle the situation that you described effectively. With perhaps the exception that you let it cause anxiety/anger on your part. Try not to take such comments personally.
Some people may give you good information. Listen and accept anything that might be helpful. Giving information is more acceptable than rude criticism offered by your aunt.
I have been in situations during which a young child was gearing up for being out of control. Sometimes this is in a restaurant. If I can think fast enough for a diversion I offer it, by doing the diversion myself. For example I may point to a big balloon and ask what color is that? Or stooping down and asking the child a question about something they're carrying or wearing. Sometimes mothers look at me gratefully. Others glower. I leave if I get glower.
I started doing this after noticing that people did this for me when I was with my daughter who was acting out. I really appreciated it.
sounds like you and I have a similar philosophy for managing children in a positive way. If Someone else doesn't agree with it, it's their problem.