This could get very long so I will try to keep it brief:
Backstory is that parents divorced nearly ten years ago, badly. Dad was a dickhead, ran off with other woman, kept mum dangling etc etc. Mum was and is a difficult woman, but he was really horrid.
My DSis and I barely spoke to him for six months or so - she was 15, I was 18. Frankly he didn’t make a lot of effort to stay in touch. He just wanted us to meet the OW and see how great she was. We refused, he said we were being unfair, etc. He married OW a couple of years later. We did not go to the wedding but did eventually meet her.
Since then contact has been sporadic at best - they lived abroad for a while. He phoned every 8-10 weeks or so with a ‘sorry I’ve not been in touch for a couple of weeks’ and so on. When I was expecting DS1 DH and I got engaged, and met him for lunch. Told him the news, he seemed pleased and among other things offered to make a financial contribution to the wedding. We said that was kind, all seemed ok. Then two days later he sent me a lengthy and horrid email saying I was throwing my life away marrying DH as he's ‘only’ a policeman, shouldn’t have DS and should have an abortion. And also I’m fat 
among other things. So then I didn’t speak to him for nearly a year - he didn’t meet DS when he was born. I eventually got back in touch because his mother (my Granny) told me she was upset about the situation, and DH persuaded me to give him another chance.
That was 4ish years ago - since then I feel things have improved slightly. I’ve tried to do as he’s asked - including his wife in things etc, inviting him to meet DS1 (and now DS2). Then this Christmas he asked what I’d like for Christmas - I suggested a book, which he sent me, and he also sent some pirate playmobil for the DSs and some beer for DH. I sent him and his wife a book each, and a couple of Berts Bees lip balm sets to her daughters, his step-DDs, who’re about ten years younger than DSis and I. He sent me a cheery text on the 23rd asking what we were doing for Christmas, but my phone had broken. I got the text on the 28th when it was repaired, replied, explained about broken phone, wished them all a merry Christmas and thanked for the presents. Then a couple of days later I tried to call. Then I tried again. And again. I get periodic texts saying ‘sorry tied up, call you tomorrow’, but he never does. He has also forwarded an email from my uncle about some uninteresting legal stuff to do with the trust of my grandfather’s estate. But otherwise is incommunicado. I keep wracking my brains about what I’ve done wrong. I went to see other family of his on the 24th but didn’t see him over the Christmas period - but he never invited us or suggested meeting up, and is usually away for Christmas so it didn’t occur to me! DH thinks that’s the problem - that we saw his brothers/ my Granny and not him - but we never see him over Christmas and he never asked! I’m wondering if he was somehow offended by the gifts, but I thought they were innocuous?!
Anyway I’ve since discovered he sent my sister a letter for her birthday in December saying he’s sorry she no longer wants him in her life, but his door is always open. She is bemused as she never said anything of the kind. He and his wife were invited to her wedding last September, but his wife refused to come as her Dds weren’t invited. But we’ve only met them about five times and there were only 12 people at the wedding in total! Our cousins, close family friends etc who she’s known her entire life also weren’t invited. Dsis explained this to dad and said she would of course have invited them to a larger wedding but as they were keeping it tiny the invitation was only to him and his wife. He said he understood but his wife was offended and wouldn’t come. He asked Dsis to make an effort with his wife as apparently she wants a better relationship with us - so dsis sent her an email suggesting meeting for lunch one day, to which she got a reply that his wife was ‘busy atm’. And nothing since except the weird letter on her birthday. But at that point he was still apparently talking to me fine .
My birthday is on Tuesday and I’m literally dreading getting some sort of horrible letter like the email a few years ago. I had Pnd after having DS1, partly but not entirely due to the situation with my dad, and since he’s stopped talking to me for reasons I cannot fathom my anxiety levels have gone through the roof and I’m depressed again, back on a higher dose of medication. We had a very up and down year last year with DH having a bad health scare, being moved by his job three times, we moved house and we’re at the point of exchange to move again when the health scare happened so had to pull out, DS1 is being investigated for ASD and DS2 arrived (which was obviously lovely but not exactly unstressful). I was really hoping 2018 would be better but now apparently my father has decided to be weird again and I don’t actually know what I’ve done wrong!!!!