you don't have to be in with the school mums
but you can ask around, is there someone with a 14 yr+ (girl) looking for extra cash, whom you can get the mobile number of and of her parent(s)?
That sort of thing.
Try and look at this at a different way, looking into what you are offering not looking out.
You are saying you want a relationship, not casual, but with someone who you only see part time during school hours, during term time in the week. That's what you are offering for a "relationship".
Would you date you OP?
You are a single mum with two kids, so if the relationship progressed they would be taking on you and your kids eventually.
When I was single my not to be crossed line was "no kids" - I wanted my/our experience of first baby to be ours. I was late 20s then so age makes a difference, if you are desiring men 40s+ it's more usual that they will have formed or you will have formed a relationship that has been settled enough to have children in.
That is not to say there is no hope. There are men out in the real world who are all shades and if the time right now is all you can offer, and they are into you enough, and you can navigate the situation to become something more solid and intertwined then it's not impossible.
You put your children and their safety and emotional ties first, they are all good qualities, but if there isn't space for an independent relationship to blossom you might have to wait until you and your children are in that space. It won't be forever, until the oldest is 14 or so. If you are not willing to get a babysitter, or their dad isn't every other weekend, or your time available is just very limited basically you may have to be the patient one and wait it out. Or wait until you meet someone who blows you away and you blow him away and the sacrifices are worth it.