He has a family, he doesn't want a second one.
OP, imagine how are you going to feel in 5+ years' time when he hasn't changed his mind and you still have nothing to do with his DS (and potential future grandchildren).
I could imagine that a son who has seen his mother go through bereavement then divorce could be extremely loyal to her and not want to see her hurt anymore and if that means excluding you then so be it. You are not, for a long time maybe, going to be seen as anything important in their family. It is not as though you're a stepmother in the normal sense, where you've had a hand in the upbringing of the DC.
I am really sorry if this sounds harsh. Please trust me when I say that I write with kindness because I think you are pinning hopes falsely and could fritter your last fertile years away.
Think ahead to future family events: weddings, babies, christenings etc etc. There is so much potential for you to be left out. If you are happy with that and will forge your own life, and genuinely OK with never having children of your own, then fine.
I'm not sure exactly how long you've been with your DP - you mention DS at 16 and now 19, so I'm going to presume at least 3 years. Frankly, if you haven't met his, now adult, child yet then I don't think anyone (other than you) is particularly bothered by this.
For what it is worth, every single one of my relationships has seemed really special ... until they end.