Yeah, take all your points but sometimes when people maintain their boundaries so very firmly it can come across as basically somewhat uptight/ungenerous/tiresome/neurotic
@Voodoo43 Perhaps so. I can definitely see how it might come across and, in my case, I'm definitely neurotic and have debilitating anxiety.
My twins and I have sensory processing differences, so we all find it hard to cope if there is more than just us and the cats.
I think I read above that the Mum had once said to you that both her twins need to be invited and I did think that was really unfair pressure on you. And, if her two are pretty much trashing your flat anytime they are over, that must really wear thin. I think you've done well to cope as you have.
I think, with us, we tend to see people out and about, as we are all pretty hyperactive (although I've got impaired mobility and some other health stuff), so we're just known for seeing people around parks and events etc. I definitely see that other parents most likely see me as odd, but we've got a circle who accept (tolerate?!) my eccentricities.