I think I can relate, if you take your friend's child out of the picture. My friend's DD, at about 3, started REALLY asserting what she wanted. And quite often what she wanted was me, GONE. I visisted too much, in her opinion, and that peeved her b/c she wanted to play with her mom or other people.
I figured it was normal. I'm the oldest of 5, and all the sibs seemed to go through that at some point. Especially with the youngest three, b/c I'm so much older than them, it would often turn on me, telling me to go home. Or maybe it's just me.
Anyway, I think it's pretty normal. It feels bad, b/c it's hurting the other girl's feelings, and it's keeping you from seeing your friend. My friend and I did slow down our visits for awhile, and at the time that was a bummer, but really, when you see each other that often you're not really talking about anything of substance, you're just blathering. Or maybe that's just me.
As the friend's DD got older, she changed out of that "go home now!!!" phase and was able to have multiple friends. I think that might be part of it too...I don't remember being able to have more than one or two friends at a time, like the differences between them were too much?
I don't know that the other girl was emotionally blackmailing, and I don't think your friend is, either. They are both communicating their thoughts and feelings, which is good! If the other girl wants to hug and is used to a hug, then it *hurts* her to not receive it. She'll either realize that not everyone hugs and get over it, or will in the future only make friends with people who will hug.
Kids get really used to what they are used to, if that makes any sense beyond the obvious. Each of my friends had different routines, and if I'd come in to babysit and did something different, ooh boy that was not just different, it was WRONG and had to be changed. So if the other girl is used to hugs, then no hugs feels WRONG to her. It's probably just what she's used to. As for your girl not wanting it, well, she's just different. I have had a friend all my life who stands FAR too close while talking (made worse by bad breath, at least as a child). It bothered me, but never too much to end the friendship or even talk to her about it (though once I started singing The Police's "dont stand (so close to me)" while she was talking to me). She wanted to stand close, I didn't, we were just different people.
Anyway, it's complicated b/c of the two women and two kids thing, but if my experience with my friend's girl is anything to go by, it's pretty normal for her to start setting those "go home! I don't want to see that person!" limits.