It's a hard question to answer. In my case it was around thirty years. I was alienated into hating a parent, though I always had contact with both of them (sometimes whether I liked it or not). I don't fall into the category of young children who are cut off from a parent.
Having said that, all I can tell you is that the child only thinks they hate you. You might have to just wait until they grow up before they put two and two together and realise what has been done to them. If you don't have contact with them, that's probably what's going to happen anyway. If you do have contact with them, the most important thing to do is remind them that you love them. The second most important is to never, EVER join in. Don't play criticize the ex, even if you want to put out their eyelashes. As I've said before, find a safe outlet for anger but never let your children feel it. You're just supporting the ex if you do. The ex ie the alienator will have told your kids all sorts of rubbish about you so by even perhaps defending yourself in a critical manner (ie, "S/he always says that but it's CRAP. S/he's talking crap"), you're supporting the ex.
You're entitled to two copies of school reports and letters home. You're entitled to have these things sent to you directly. Offer to join the school run or clubs run. Offer to pay for a club or two. Attend everything you can and send good luck cards etc when you can't. Give gifts/cards/letters directly to your child. The mailman will deliver but the ex may or may not.
If you can possibly avoid things getting nasty, do, even if you eat more humble pie than you think you deserve. Your kids are worth it, aren't they?
My ex is also the child of a rotten divorce so, despite our mutual loathing for one another at first, we managed to work our relationship into something pretty decent because we were absolutely determined our offspring would not be victim of PA or even of warring parents without PA involved. It was HAAAAAAARD, probably the hardest thing I've ever done, and we are not perfect, but our offspring knows where we are, that we both adore her, that we plus stepparent want what's best for her. If I ever think he's trying to out-gift me, I say "Wow! That's soooo cool!!!" instead of "You're trying to out-gift me", although I have to say it rarely happens. We did have moments after the break up when he DID try to play the "Criticize the ex to all who will listen" but as most of those people are HIS friends and family, I learned none of it matters and put it out of my mind. He also tried it on me: he'd call me from his new partner's parents house to loudly berate me about the offspring's dirty feet (!). It was all posturing and I knew that and he knew I knew that so I said (with gritted teeth and clenched fists) "I'm not playing this game! Do you want to talk to the offspring?" A couple of episodes of that and he stopped. I wanted to whack him over the head with a rolled up newspaper, but it stopped.
So, back to the original question. The answer? I just don't know. It depends on how you handle things, whether you have contact with the kids, whether your ex will calm down, the courts, all sorts of things. Just don't engage the ex. Be as conciliatory as possible about everything, if you want your kids around. Forget your ego and your pride. Love those kids and SHOW them as much as possible. If your ex bans you from visitation, go to school plays and make sure they know you're there. In the long run, all this will add up and they will understand, at some point, that the alienator is a liar. That you have always loved them. Set up a website or a myspace page or something RIGHT NOW so that in a year, two years, five years, whenever, they will see that you have loved them all along.
My mother put up with me despite my hatred for her. I had everything I needed while I was growing up. She and I may disagree about disciplining our children, but she never let me down, not even when I was an adult.
One thing I would change is something I mentioned previously. She stayed silent about the alienator. She never defended herself, not even wisely. She just ignored everything he said and did, and everything I said and did, so that when I was having rages, she didn't try to get to the bottom of them. When I said "I know you don't love me!", she said "Don't be silly" and walked off. DEFEND YOURSELF but don't bitch about the ex at the same time. It's not an impossible task. Is it?
It will end one day. I can't tell you when. I just promise you it will. Your kids aren't stupid. They'll work it out.