Little back story... parents split when I was about 4. Me & my sister spent every Saturday with him for about the next 15 years, during which time he was with my first stepmum. They split in about 1996, and he married again. We all had regular contact all over that time, although he'd moved away. He split with my second stepmum a couple of years ago. With me? 
The last time I saw my Dad was on New Years Day 2010.... he came to stay overnight, and spent the whole evening texting someone, and ignoring my children, which really fucked me off - I didn't say anything though, pasted a smile on, and got on with it.
We had pretty much no contact after that day for months and months - fast forward to Aug last year, when he called because it was DS's birthday - he called in the afternoon, when DS had gone to his dads, and I ignored the phone because I was busy doing something. He didn't leave a message.
Later on that evening, he sent me a text - something along the lines of 'I can't believe you stopped me from speaking to my own grandson on his birthday... 'blah blah - I called him immediately, but he had switched his phone off. So I sent a reply telling him that I had been out when he called
- and he replied telling me that he'd called 5 times, and left several messages.
Now I KNOW this is a lie, because I was there - but because I lied and told him I was out, I can't pull him on it.
He called me Christmas week last year and asked us to all go down and stay at his for a couple of days - Christmas Eve was the Friday and this was the Tuesday
so I explained that was impossible, and that I was working right up until Christmas Day - he told me that it was either that week or not at all as he would be too busy opening a new business in the New Year and wouldn't have time.
So now it's nearly May. I still haven't called him, I'm by turn angry and sad, and I really have no idea how to move on. I have to make contact for my children, and because he's getting older, and because he's with yet another new partner that I haven't met... but I don't know what to do. If I call him, I'll lose my temper.
Can someone advise me? Sorry this is so long, and that the circumstances sound so incredibly petty. But this is the last in a long line of.... difficulty.. in our relationship, and I'm stuck.