Sounds like the aunt got to her. Very stupid of her to lie, but she did at least admit it to your dh straight away.
You need to think about what you want from this long term, because obviously how you handle it now will affect how your relationship goes in the future.
Go in all guns blazing. That's probably what she was afraid of in the first place and made her lie. Your long-term relationship will be ruined.
Brush it under the table and never mention it again. You will never trust her, which will have long-term effects on her relationship with you, with dh, with dd.
Only communicate through dh, but never see her again yourself. Again long term effects on her relationship with dh and dd, and no relationship at all with you.
None of those are good outcomes, imo.
Now you need to heal this wound, I suggest you get the anger out of your system, maybe by shouting at dh a bit, or maybe by going somewhere and just screaming for a bit. When you're able to be calm about it, have a chat with mil. Don't be angry with her as yet, try to find out what she really feels about vaccines and what made her do this which includes lying to you about it.
Basically be an adult, have an adult conversation with her.
Of course, you can express your hurt, surprise and anger to her, she'll be expecting it, and it is best to get it into the open. You can also remind her that it will take you while to get past it, but that you want to.
Much the hardest route to take I think, but the one most likely to ensure a happy future for all of you.