YANBU!! My neighbour did this with my DS when he had a new bikee.
DS was about 7 and was at the top of our road where it is safe to sort of cycle round practicing.....my neighbour stood outside his house and was shouting to DS to come on, show him what he can do, how fast he can go etc etc........DS in a moment of madness cycled down towards him at a right old speed (down a slight slope too), went out of control and rode into his wall. Sounds funny now but believe me it wasn't at the time. I just knew it was going to happen but it was all so quick. Thank god DS had his helmet on.
I just said to the neighbour what a bloody stupid thing to say.
OP she doesnt sound like a danger but just be careful and keep an extra close eye on DS when she is about. She just sounds strange.
I'd avoid contact with her, not because I think she is a danger to your child when you are there, but because you know her to be a bit odd and you know her to be a liar. Spending time with her doesn't make you feel good, so don't do it.
I don't know what's strange about being able to see a 2 year old when in a park. I never let mine go that far away from me. Though I can see that as he was with another adult, you'd expect that he was safe.