Your initial approach to get to know people might be a bit OTT.
A weekend "lunch" is not obviously that child or family friendly.
They don't know you.
We all know from experience, that your children's friends' parents are the people you're most likely to socialise with for all the years through school.
But if I were you, I'd make it bbq, not sit down lunch, and all activities focussed on children either in the garden or inside (weather dependent). Just make it about the kids - because right now that's the only thing you have in common.
For those adults not able to attend, I'd still say children welcome.
My children are all grown up, but if I was invited to an adult-focussed lunch by a parent of a classmate who I didn't know so well, I'd be wary.
Sometimes you have to let things progress at a natural speed. And when you have children, you can have enough play dates to really get to know mum and sometimes dad and click with them, and work out if you want to spend your (valuable free and family time) with them.
Just, was the lunch mainly for you as mum and a person?
Because if it was, it is OTT for other parents who are not yet your friends.