Honestly, given your story and the reaction of the two people involved after this incident, it sounds like you were minding two three year olds.
You've got a little 3-year-old girl who is being tickled by 69 year old grandma, when she was finished being tickled little girl says "I don't like you" and Grandma burst into tears and goes running into the bedroom and is causing a gigantic fuss. And you say this is not the first time she's done this in fact she does this all the time. That she's extremely reactive, never positive, very immature, and in your words, you dread being around her because of her behavior.
If there's nothing you can do about Grandma because she's a lost cause, I mean you can try to explain to her that a three-year-old says things like this, get over it, but in my opinion, you're better off focusing on teaching your daughter a lesson here.
That while it isn't nice to say things which might hurt somebody else's feelings... But also, it's important to stand up for yourself. Perhaps saying "I don't like that, instead of I don't like YOU" would have been better (yes I know she's only three a little young to be making this sort of distinction but you never know, some three year olds are brilliant) and just focus on your daughter in this case, giving her the tools that she's going to need going forward in life to deal with difficult and immature people. Her grandmother is obviously going to be a recurring problem and great practice for other immature kids who she meets along the way, to practice her correct response with.
I'm so sorry that your mother-in-law is an adult toddler. I know a few of these people. It's incredibly frustrating if there's no cognitive/psychological issue involved, and it's just them being insufferable.