I think it is simply a matter of, these friends of yours don't understand. It doesn't sound to me at all like your daughter was manipulating you. Yes, they understand how to do that at their age, but this doesn't sound like that sort of situation. I agree that when you go with THIS group, it would be wise to get a babysitter for your little girl, but not because they think you should, but because it will allow you to relax and enjoy your visit and not feel like they are assessing your every move.
I would have been mortified too! My brother does this when he sees my kids act up or be shy or act too goofy. Childless people tend to have this vision of what they think their kids would act like and that a good kid is one that sits quietly and colors for 3 hours straight and never bothers anyone. Guess what? I have one of those. But my other 3 are normal. :) To me, that means that no more than 1(probably less)out of every 3 kids is the perfect, manner-minding, sweet, outgoing but contained, crayon wielding Michaelangelo.
My boys both had a really hard time meeting new people. Even after being around them several times, they would still seek me out for reassurance and entertainment(even if I was only steps away). Let's face it, how fun was it when we were little to just sit all alone with the drone of strange adults in the background with no understanding of exactly how long we would be there. We didn't know if it would be seconds or hours. Why is it so hard for adults to remember what it was like as children. There is nothing wrong with teaching our children that there are times when they will have to yield to what we are doing (which sometimes means boring adult visits). But I also think adults automatically assume that we are giving in to the whims of the child by limiting time spent doing boring things, when in actuality, you taking her and leaving was so kind and thoughtful of you. I think you did the right thing. She did what you wanted for a long period of time (for her), so in return you took her to the home that she loves and is comfortable in. You taught her how to do something nice for each other. She has to go with you sometimes, it is good that you don't force her to do it all the time and that you realize that she won't be little very long and it won't kill us to cut back on adult time a little for the few years they are little kids and only want their parents.
As far as making her adapt to different situations. My oldest daughter was very independent, would go to anyone, do anything, color and be quiet and perfect for hours if I had wanted her to. The other 3 are very normal kids that are always hesitant the first time they do anything. My 3 year old is the shyest kid on the planet until he decides it is something that he really really wants to do. With him, I have to just ignore the fact that he is shy and go in and start doing the thing I want him to do and pretend that he is too little to do it so he'll decide that he does want to do it and it's safe for him. He won't eat anything unless he sees me eating it too. Before too long he is over there telling me to let him do it and then he will eventually get to doing it on his own without me anywhere around. When we leave him to be babysat, he is the same way. He does great with people who take the same approach to it that I do. People who hover over him and coddle him or just try to force him, he won't ever go near again without throwing a hysterical fit. It isn't because he is stubborn (like I've been told by some) it is because he doesn't feel safe and reassured (by example) that it is safe and okay. He is just one that wants my reassurance and as soon as he sees me enjoying the activity, he is okay with it.
On the other hand, this is the only 1 of the 4 that will try anything at home, in his element, and has the best sense of humor and the most natural athletic and artistic talent. I get a lot of parent-pity looks and sneers from people that think I don't know how to control my child. I have to just remind myself that someday he is going to be a great great person and that right now they just don't understand that you cannot force shy children to emerge before they are ready. They are a breed all their own. Force and control make them more resistant and lengthen this phase of their lives. The way you get them to outgrow it is to love them through it and don't coddle them but treat them the same way you would if they were responding to every word you said at home.
Example: Little Susie doesn't want to play blocks with the other kids because she is afraid to. So you pretend you don't see that she is being shy (no: "it's okay sweetie, mommy is right here"). Just go, "Oh hi guys! Can I play too?" Yes, this is where you sit down with them and start playing. Put a couple blocks together and then very non-chalantly ask Susie to hand you the one that is "over by that box" (closeby location). If she doesn't, ask another child to get it. The next time, or so, you can bet she will go get it. Even most shy children do not want anyone interacting with THEIR mom.
It is hard sometimes to do this when it is so nice to feel validated by their clinging hugs, but this is the best way to help them learn how to function in our increasingly crowded world. Even the shy ones will have to grow up and learn to function without us someday. Good luck to you and know that you aren't alone and I know you will do a great job with this! Keep up the great work fellow mom! :)