That happened to me with my late husband's kids. Two of them - both adults by the time I met their dad. Their mother had an affair with someone from work, but convinced them that she'd gradually become close to a friend from work...She's currently with partner No.4.
Dh got more upset about the birthday thing than I did. One time a card arrived from the son and his partner. I think it was a blank card they'd filled in - I suspect DH had reminded them.
Anyway, when I opened it, there was the greeting written by the son's partner and below it in a different pen colour, the greeting written by the daughter.
I remember Dh looking at it incredulously: "What's wrong? Could they not afford another stamp?"
One year, a lovely bouquet of flowers arrived. DH was so happy: "What does the card say?"
They were from my SIL. Dh was absolutely crestfallen.
I got flowers from the kids once: their mother's 3rd partner had died and I felt sorry for her. She needed a day operation, so I volunteered to take her to and from hospital.
I got flowers and a note that said "Thanks for helping Mum."
On the way back from hospital, the ex told me that she was going away for a birthday weekend with her daughter and granddaughter. I said, "Oh, that's nice..." thinking that it was a lovely multi-generational girls' weekend away.
Then we saw the FB pics: DH's ex, daughter, granddaughter, son, son's partner and daughter's best friend.
DH was disabled by then, so maybe that's why we weren't asked. He did ask his daughter why he'd not been invited the next time we say them: "Oh...I didn't think you'd want to go."
The more I think about it, the more I think they didn't want me there.
DH died during lockdown. They told me they couldn't come to the funeral. The son had been told to shield (true); the daughter told me she had adult-onset asthma and she thought it would be too upsetting for the then 20 yr old granddaughter. Nevertheless, they wanted their say in the funeral.They asked if their mum could represent them. (I later found out that that was her idea. )
Side note: when the gd was born, I was told I was too young to be granny. DH suggested I could be an honorary aunt. Nope. She had 'plenty aunties' - her uncle's partner and her mum's best pal.
The mum's affair partner was 'Grandad'. When he died, the gd's father complained to us that the AP had left all his money to the ex. Something should have been left to the granddaughter, because she called him 'Grandad', apparently.
Anyway, I cracked two months after my husband's funeral. TBH, I had a complete breakdown. They've gone Non Contact.
I made sure that they got their inheritance. The only time that they got in touch was when 2 of them phoned the solicitor to say that their cheques hadn't gone through.
What did I do about it, OP?
For 27 years, I kept the peace, bit my tongue...and then cracked up after the funeral. I used to go half with DH for birthday presents, though latterly I told DH I would no longer contribute to presents for his son and daughter.
I sorted through my MIL's jewellery for DH and had pieces mended for the granddaughter. When it looked like the kids were not going to get married, I gave them the money that I'd saved for their weddings.
I'll not monopolise your thread any further, but being nice got me nowhere, though they were nice enough to me (for the most part) until I cracked up.
I do recall one time when we had a meal with the daughter, gd and the ex, the daughter saw me with a bank card: "I'll go half!"
"Oh, it's been paid."
"I'm not a CHILD that has to have things paid for her!"
Me, nervously, laughing: "Oh, you'd better argue with your dad then - it's his card. [I had POA for him.] I just do as I'm told!"
I think that was the one real piece of evidence that she resented me. Might have been because I'm a lot younger than her dad, but there was the same age difference between her and her late partner. Go figure.