Mostly posting because that really stinks and I am sad for your dd.

Can you or dh take her to swimming, stay and talk to the other parents? You could make a connection there.

Not to derail but:
"i honestly do.not.have.time to do PTA or to volunteer - I work full time outside the home and am primary breadwinner. My hubs just went part time. I go to school events when I can. Dh handles a lot of the stuff."
Do you honestly think that most people don't have the same amount of free time that you do? 95% of our volunteers (including room parents, event organizers...) work full time in demanding jobs. You are not unique with your time constraints. People make time for things they value and prioritize. My dh works until 7 and then during musical season goes to help with sets and costumes until 9-10pm every night. Until he found a project he really enjoyed and valued, he'd have said he didn't have time to volunteer. He made time though for something. I really think you have a different version of what volunteering at school needs to look like than it's really like. Heck, my favorite volunteers are the ones that stick around simply for 30 minutes after an event and put a few tables away- you might not get your kicks out of that but it is volunteering, it could easily fit in your schedule if you are already at an event, you'd get a chance to talk to other parents and they would be thrilled to have you! No one wants to stay and clean up- many hands lighten the load!