To have someone just barge right into my yard like that would freak me out just from that. And then to follow you towards your house, it also sounds like she was too close and invading your personal space as well which would make anyone uncomfortable. And, if all that was not enough, to start asking more personal type questions without even knowing you, is just too much. Curious or not, you don't start any type of friendship by just going right into someone's yard and practically into their house like that. That is just too weird. I know I would have told her from the beginning to please leave as I have something I need to do and then go straight into the house with my baby in my arms. I would have then watched to see where she went to see if she even lived nearby. I would have then called the police just to have it on record in case she did come back again and maybe even try to take your baby. You just really never know.
It is possible that the woman just doesn't know how to properly introduce herself without being so overwhelming and overbearing. But, from your description, that incident would sure make me leery of her.
