OP, I rejoined Mumsnet just to tell you my story and give you hope.
My marriage broke up when I was your age. I had two small children. For the next few years my love life was DIRE - I had a couple of lowering flings with porn-raddled bachelor sharky men met through OLD and real life, and the few men I did like didn't want me. So I basically thought, well that's it for me then, this is what it is being over 35 and a single parent, and so i gave up trying and didn't have sex for three years. I honestly thought that my ship had sailed, and I (almost) came to peace with it.
Then, when i was 40, not expecting anything, I met a man through work. He was my age, single and extremely attractive, and so i was wary, assuming he would be another of these broken grim player types. But he wasn't - he was just in a very similar situation to me (divorced, child) and after a few years of being single was finally ready for something serious. He was - is! - a truly special and completely non grim person, and five years later we are married and still madly in love. It's in a completely different league to my other relationships, including my first marriage. He is brilliant with my children, and I am very fond of his. We're too old to have one together, otherwise we'd have tried to do that too.
So don't give up. Or rather maybe do give up, because it's a lot less exhausting and potentially depressing way to get through the day, but stay open to being surprised.