You didn't know, and if she were REALLY THAT concerned, she could have easily declined to go and taken her kids home. I have to be honest and say that I don't have allergies, nor does anyone in my immediate family. But, honestly... You gave her the option to speak up without offending you (you ASKED her point blank if it was a problem) and she said nothing. And she chose to go ahead on the hike.
Sure, she was probably worried about her boy(s), but that is all on her, not you! You did nothing wrong.
And the analogy of bringing peanuts along as a snack and the kid(s) being allergic to peanuts is a false analogy. A pack of peanuts is not a living breathing creature.
You could probably make a reasonable argument that SHE should have declined to go so that you could enjoy the hike without feeling awkward about having your dogs along. It was a public trail. What if some other hikers were there (not part of your group) just a little ways in front or back of you that had their dogs with them? Should THEY feel obligated to take their dogs back to their cars? Unless the trail is posted "no dogs" then she should expect to encounter them and not be a woman possessed about it.
This is a woman who knowingly chose to put her allergic child in close proximity to his known allergen. Granted, she didn't know you would have the dogs there, but she certainly knew that OTHER people might... I'm not saying she shouldn't have come along from the start. But once there, and realizing the situation, she could just as easily packed up and left as you. I'm not familiar with NM's topography in the mountains, but I'm thinking I'd be worried that a THREE YEAR OLD would slip or fall and get hurt on a hike in the mountains. I'd say the dogs were probably more in their element than the 3 year old. An older child can keep up and is better coordinated, a younger child can be carried in a pack, but a 3 year old... that just sounds like an accident waiting to happen to me.
Oh, I wanted to add: It sounds more like she just doesn't LIKE dogs. Perhaps she has so fixated on her son's allergies to them that she overreacts and has now transferred that to her kids who also may now be fearful of them. Not all kids like dogs. Some are quite fearful, some are just uncomfortable, and some LOVE them. But as parents, we sometimes sway which way that all plays out by how WE behave around them (even unintentionally). And it sounds like she just doesn't like dogs and would prefer not be around them. Maybe even from her own childhood, having nothing to do with her son's allergies. She might be used to using his allergies as an excuse these days though...