I feel your pain, DDDDDora, and (by accident) I may be one of the mums that you aspire to. So here's my history:
I was NEVER a popular girl. All through school (different schools cos we moved), I was NEVER the cool kid, and sometimes I was the kid it was socially acceptable to despise. So please don't go thinking I'm some kind of super-confident uber mum (although, I do now have posts on S*B, so I have moved on, but that's a different thread!)
When our DD (and we only have the one) started at primary school, within the first few weeks posters went up around school advertising for the PTA meeting. So, because we wanted to support our DD through school, we booked a babysitter and we both went (we laugh now at how earnest we were!). As we walked up to the classroom where the meeting was, we could see all these chairs laid out and an empty room, and my DH was hissing at me "don't volunteer for ANYTHING" and then they opened the wine....
Well, we got slaughtered! Volunteered for EVERYTHING.
I'm SO glad we did. Helping at events gives you a 'role'. For the first time in my life, I felt comfortable to rock up at an event (ok, it was the valentine cake bake!) without a friend in tow, not knowing who would be there, but knowing it would be ok.
So, JOIN the PTA. You don't have to commit yourself to anything you can't deliver. They will be grateful for anything. School will appreciate you. You will have a role (i.e. a reason for being there) and you will be 'busy' (selling sweets or picking up litter, no matter...you will find you belong) And you will get to know other parents. And insecure people will appreciate you.
The incident with the 4 mums ending up at a coffee shop sounds like confused people worrying and ending up bonding together. THEY sound insecure to me. It's not a slight.
The other thing is to suss out the children your DC like and start inviting them (individually) back for playdates. If the kids like them, then they will come back. When parent comes for pick up, offer them a cup of tea. Say things like "you have to watch this" (their interaction).
Like I said, I was never a popular girl. My child is, and by extension, I'm a popular parent. It happens by accident.
Good luck!