Foinaven I honestly don't think you'd ever gain access to the inner circle of mums because of the simple fact you're a man. Sadly.
I know several dads who are the main carers and they report the same problem you highlight. They're very much liked by the mums at the school gates, arrange play dates etc, but are never invited into the inner circle. The main reasons being husband jealousy, intimate female conversations and a kind of sub-concious mistrust.
Oh I really feel for you, it's really hard to make friends at those parent things at the best of times, let alone being a bit of an odd-one-out. Do keep trying, though. Perhaps even use the opening line "I always feel like the odd one out at these things..."
Well I wouldn't be too put off by the 'pat on the head' thing. She is obv. a bit socially stunted and insensitive and prob. other women there may have judged her for it! I imagine it may be a bit hard to 'breakthrough' as the only man there, but there will be lots of others there also finding their feet and a bit unsure.
I'd take the long view - if the novelty of having a man in this 'circle' becomes a public issue then make up your mind about what you are comfortable with. The fact your a man in a predominantly female setting is something you'd have to adjust to on MN anyways.
So, a week or so ago I was informed by DW that there was to be a pub outing for parents of Primary 2 and that it would be fun to for us both to go. Sleepover arranged for DD we trundled along to the local, got there pretty early, sat talking to the mums I know from playdates etc.
As the evening went on more and more mums arrived, still no dads though. When one of the newly arrived mums (not even from P2!) virtually patted me on the head as she called out 'hello ladies and er man' I decided that I'd best make a tactical withdrawal.
As I am 'primary carer' for our DD I found it rather difficult to gain the 'trust' of the mums regarding playdates last year and made a conscious decision to put myself out there more. This year I have been pro-active in arranging playdates, and it seemed to be working, to the extent that my DD has a far more active social life than I ever had.
I realise with hindsight that the reason my DW received the 'pub email' and I didn't may have been a subtle hint that men are surplus to this particular gathering. Or that may be my well-balanced attitude showing through (chip on both shoulders).
I suppose I'm asking should I have been annoyed or shrug it off? To be honest I wasn't annoyed, more sort of bemused by it all.
Having typed all the above and read it back I think the question I am really asking is how does a dad who decided to be the 'mum' gain access to the inner circle of mummies and should I bother?