Medford, I think you can listen to your daughter tell you she doesn't want to go, she just wants to " stay home all all day" and then after you listen to her once, you say "Well, we are going to go play at the park, we can't stay inside all day. I know you love to sit on the couch but we are going to go to the park and play on the swings" then you stop listening. And set the limit "mary, I heard you the first time, we're all done talking about that." "I'm done listening to your whining. Let's talk about something else." I wouldn't keep entertaining it, or responding to it. "I'm not going to listen to you when you whine. You need to use your big girl voice."
sigh. it's a long, uphill battle, though! the thing I hate the absolute mostest in the world is whining. Really, I get a physical reaction to it in my stomach. My niece whined, whined, whined with my sister, but I was really clear and she didn't do it when she was around me a lot. I'd have to spend a day reminding her I didn't listen to it, and I wouldn't, I would just keep walking around the house, doing my thing getting ready to go, whatever, and she had to run to keep up, but I wouldn't look at her or respond until she stopped. That's after explaining why we were doing the thing, or she couldn't do the thing, whatever. My sister would calmly stop everything she was doing and explain for the 100th time why, and my niece got so much attention from it, so of course she kept doing it. And then the other 1/2 of the time, my sister would give in to the whining, so of course that trained my niece to keep trying, since it worked quite a bit of the time!
And standing and staring at you (balefully or not) while you play with brother at the library is better than whining and stomping her feet!
You and IPW have a cautious, slow to warm up kid, that's probably not going to change, but giving them lots of opportunities to practice and do it again and again, and sometimes doing well (playing in the bouncy house, going skiiing) and sometimes not (leaving the bouncy house when another child enters, not skiiing the 2nd time) is part of the package.
medford, eventually it will be great for your daughter to take a lesson or two, but I'd wait until she was 6 yrs old at least, and then think about the kind of lessons - perhaps ballet where there aren't too many kids and where they are kind of more orderly vs. gymnastics with tumbling and scary physical stuff. Or taking music lessons where you sit in a chair in an orderly fashion and each have your own instrument vs. having to grab and get them from a pile in the middle. Thank goodness your daughter goes to childcare, where she is constantly with many children, having to deal with it, that will make kindergarten so much easier for her, seriously. I know her transition to preschool was hard, but this is a time where what she is most learning is all that social skill stuff, time to learn to read is in elementary school, and having her learn all the social stuff now is critical so it doesn't get in the way of her learning in elem. school. Still, she'll always be shyer, and hang back until she observes others, and that's fine, as long as she eventually does try the thing.