Your age is likely to have an impact but perhaps not in the way you think. I was really interested to read your responses to others to get more of a feeling of where you're coming from and these are my thoughts...
I'm in my mid-late 30s with a child about to start school in September. I already have established friends (dropped some, picked up some over the years) but ultimately I'm not at a point of trying to seek out friendships (and I expect many of the older Mums are in the same boat). I've found, having that laid back attitude seems to attract people more than when I was younger, like you, and wanting/trying to make friends. Someone mentioned, earlier, about a younger parent possibly wanting someone to lean/offload on, rather than be an equal friend with and I think there's perhaps some mileage in that. At my age, I'm definitely past that - life has finally levelled out and calmed down, and I'm ready for a peaceful, drama-free few years before we get into the realms of caring for our parents!
There's also the question as to would you be wanting to make friends with these Mums, if it wasn't for your children being at school together? As many people have said, having a child the same age isn't enough of a reason to become friends... Especially if those older women already have established friendships elsewhere and aren't on the lookout, as you are, for new buddies. I appreciate you've noticed some of the newer Mums being included ahead of you but I'm guessing that's because they would be friends regardless of the children.
I think your perspective sounds very immature. I don't mean that in a derogatory way - it is a simple reflection of your age (and that is no bad thing). You worry about the size of your house - I lived in a small house, then an average house and now a big house. I could not care less what size house someone else lives in. I think part of that comes from not being a dick and part of it comes from being at an age whereby my whole life is fully established and balanced, and I'm so content that there's no need to compare with others/be judgy (which is what those who are insecure and not content with their lives tend to do). What I would be concerned with is whether your home is reasonably clean and tidy.
That brings us on to parity - you have been to others' homes but never returned the invite. No one understands the reason for that but see it from the other side. At best, it looks as though you don't care, at worst it looks as though you're taking advantage of others' hospitality whilst not being prepared to be the host.
If someone I barely knew asked to meet up somewhere like the park or soft-play, I probably wouldn't go. It's more of a faff, potentially has cost implications (which I wouldn't object to with someone I know) and I'd feel was just generally a bigger commitment than going to someone's house. Those are also the sorts of things I'd prefer to do with my child alone. If that same person invited me and my little one for a playdate, I'd do my best to make that work (though my diary is currently ridiculous with plans made months ago with family and friends!).
Being honest, I wouldn't automatically feel drawn to a teen Mum. I got married, persued academia and a career. My husband and I waited until we were financially stable until we had a child (to the point that we may now be too old and/or unable to afford a second child). I would certainly question your life choices and how they jar with my own views of right and wrong. Life choices would also merge into questioning other choices, particularly around parenting styles, and whether your attitude to life is one I'd want being an influence on my child (which it would be if we were to become actual friends).
That said, I wouldn't treat you differently, if you were to approach me and be nice/fun/interesting/want to drink wine with me! I'd be interested to talk and find out who you were and, honestly, those thoughts/concerns in the paragraph above wouldn't feature. I just probably wouldn't be inclined to make the first move - for the reasons set out in all of the paragraphs above.
Interesting little anecdote from the other day... I was at a party and spoke to a woman who is known by most people where I live but whom I'd not spoken to until relatively recently. We had been interested in buying the same house - she bought it but we moved to a different house only a few doors down. She commented that she thought my husband was a bit snooty (he isn't) and that I'd only spoken to her since she had bought the house (making a comment implying that only now is she good enough to talk to). Whenever I've been out and she's been there, she's always been surrounded by a large group of friends and busy with them. She looks popular and fun, which is wonderful. I'm usually just out with my husband, enjoying a bit of couples time, and will chat to people we bump into, especially if we already know them. I have never swerved her. She's just one of many people who live here who I hadn't met, organically, until recently, and, at which point, she and I had a mutual topic of conversation to go at. I did put it to her that, just as she thought we should have spoken to her at some point previously, she also could have approached us to speak to us but never did. The important difference is, I thought nothing of her having not approached us but she judged us for having not approached her.