Getting Willow into the world, and lap-sit misadventures

One of the things Cherish and I worry about with my staying home with Willow is that she will miss out on socialization and play with other kids.
And this is a tough nut for me to crack because I am a shy guy (and many moms seem downright afraid of me). But I've been working hard at it, enrolling Willow in a play and learn class (which, it seems, might be more for my benefit than hers because I have to, YIKES, interact with moms) and taking Willow to playgrounds, parks and bigger attractions such as the zoo.
I searched in vain for a play group for Willow (I found one dads group in Nashville, but all the kids in the group seemed to be years older than Miss Willow).
I think I've succeeded, and I think I will get better at getting Willow out into the world (this summer is going to be grand and my little girl is going to start pulling her shy daddy into those awkward situations), but there have been flubs along the way.
One of them, I'm sorry to report, is lap-sit story time at the library.
Cherish and I took Willow for the first time back in October, but the experience proved much too daunting because Miss Willow was too young and couldn't play with the older kids. I waited a few months and tried again. The experience for Willow was improved but still troublesome.
Here's why:

• The kids are too big and aggressive. Some of them are 5 years old, climbing stacks of boxes (one boy fell and cracked his head on the floor).
• The big kids swarm the librarian, blocking the view from younger kids and interrupting the story reader. Sometimes, I get lost in the story.
• The big kids start playing halfway through the story, dumping boxes of blocks onto the floor and kicking and throwing balls.
• And here's the worst part: The parents chatter through the entire ordeal, stopping only to yell at their kids to "get out of her face" and "get down from there." One of the parents referred to the story time as "play group."

Dutifully, I took Willow to the story time every Monday for several weeks because she seemed to enjoy watching the other kids and sometimes she played with another baby on the floor. But when her favorite toddler friend stopped coming about a month ago, Willow stopped playing.
I talked it over with Cherish, and we pulled the plug.
I'll still take Willow to the library once every week to pick out new books, but I'll spend most Mondays taking Willow to other places, to new and old playgrounds, to the zoo, to our local and other libraries, wherever the adventure takes us. I'm calling it "Megadventure Mondays." I'm going to try to get Willow out there with other kids.
And in six short months, I'm going to try another story time at a neighboring library, where the age limit is 18 months to 3 years old.
I'd love to hear your thoughts and experiences related to this.