The OP.
No, the OP says they separated after a short relationship before DSC was born.
Entirely different to him bailing and leaving her to raise a child with no other input than financial.
Until OP clarifies the situation, none of us know.
Interesting that a woman who has enough not to work, has children in private education and maintenance (which OP HAS stated) considers herself hard done by. Even more ludicrous that she considers not having fancy holidays and children in private school to be poverty. A grip is needed I think.
If (big if) he hasn't been an involved parent, then he's an arsehole BUT the texts from the ex aren't about his parenting, they're about the life she thinks she should have had.
Giving birth to his child means she's absolutely entitled to maintenance, school fees (if they apply) and support from a co parent. If she doesn't have this, she's every right to call him out on it because he's not doing enough.
It doesn't mean she's entitled to half his pension if they weren't married, especially not 10 years later and it doesn't mean she's entitled to tropical holidays and to be able to send offensive texts arbitrarily.
OP I'd ignore anything that isn't relevant to the care of your DSC and I'd encourage your DH to do the same. Engaging with this will only continue it.