Not to go into a load of past history, but to provide context. Divorced 12 years, 2 kids who live with me. Dad is remarried w/2 stepkids - one the same age as our youngest, one a couple of years younger. NOT an amicable situation, for a lot of reasons. Kids are now 17 & 19. The kids saw their Dad regularly until ~1 1/2 years ago, by his choice.
Our youngest has always been his favorite of the two. When she turned 15, she heard nothing from him. No card, no call. Nothing. I let it be. When she turned 16, I threw her a relatively modest party. Knowing she would be thrilled if he was there to dance with her to "their song", I invited him. Didn't ask him to help pay for it - just asked him to come celebrate with her. He declined. (I still haven't told her that I invited him - I wanted it to be a surprise.) Still, though.... no card, no call. She just turned 17. I know she wasn't expecting him to call her, but she was hoping. Well... Ended up in a puddle. This, to me, was enough. I emailed him and asked him to call her. He texted her. No happy birthday. Just "hope you had a good day."
Ya know... that's just not good enough.She's not looking for a gift. But... a "happy birthday, I love you" or "hope you had a good birthday. Love, Dad" would have made her day. At this point, I'm not prepared to intervene. She will refuse to make the first move from here, and so will he. Frankly? It's not my job anymore.
So... the word to the wise... Be the adult. Even if you think the kid is wrong, remember that YOU are the adult. Pick up the phone, shoot a text, shoot an email. I understand that your ex may not be all that nice, and may be filling your kids' heads with crap (for the record, I don't - I seriously considered giving her $100 and telling her that her Dad sent it for her, just to make her feel better). But it's not the kids' fault. Tell them you love them. Tell them you're there for them. Love your kids more than you hate your ex.