I am in the middle of this right now and you are right... in many ways, it's worse than infidelity or divorce.
I have tried to spin things as a positive and the one thought that comes back to my mind is that infidelity, divorce, and parental alienation... has taught me that I really and truly love my children. I can't intentionally hurt them (e.g., by saying truthful but hurtful things about their mother) and I can't stop loving them no matter what they say or do.
As far as solutions to your situation, others have hinted at this but... you have to play the long game. Meaning, you need to set an arbitrary date in the future and decide that your goal is to have your kids love you on that date. For whatever reason, therefore, my thought is "I want my kids to love me when they turn 23 years old."
You are 100% correct that the courts are going to let the teenager decide, with the caveat that the courts might care if your ex is intentionally, repeatedly, and significantly violating the parenting agreement that you both signed as part of your divorce. So, I would (with a few exceptions) basically give up on any assistance from the courts.
So, what are you to do?
First, do not give up. If you only get one or two days every six weeks, then make the most of them. Be a Disney Dad! Whatever it takes! Related to this, send them text messages (with photos!) whenever you can and it feels natural (not forced) to do so. Attend all of their school functions, whether they say that they want you there or not. If they don't let you see them on gift-giving occasions (birthdays, etc), then send them a gift anyway. I 100% promise that your child is watching and they will remember how you are handling this. They might say things (now) like "he's so annoying! why doesn't he just leave me alone!" but you can ignore that. You are their dad and that's for life, whether they like it or not.
Second, never, ever disparage their mother in front of them. Do not tolerate anyone who does. I would also recommend that you don't go so far as to cheerlead for their mother (i.e., lie and say things like "she's such a good mom!")... just avoid that topic. Definitely try to learn about their life at their mother's house and be openly supportive of your child having a great life there. My son, for example, got a new Xbox and I bought him a hands-free headset for it for his birthday (I've never gotten to see him use it) but I ask about his Xbox, the games that he plays, and who he plays those games with.
Third, try to separate "I am a pain-in-the-ass teenager" from "I am the victim of parental alienation." It's hard because they look a lot alike, but one is normal/healthy and the other is child abuse.
Fourth, remember that your ex is making a ton of mistakes that will hurt her in the long run. I have friends whose MARRIED parents practiced parental alienation and as adults... they recognize how awful the alienating parent was. My ex is refusing to let her son bring his Xbox to my house. My ex has been generous enough to buy a new car for herself and she lets our two daughters drive the car that she used to drive, but she refuses to let either of them drive it to my house. Petty crap like this is your friend.
Basically, you're getting crumbs... and you need to cherish every freaking bite that you get, so act like it's the best three-course meal that you have ever had. Basically, you have to focus and be the absolute best parent that you can be with whatever opportunities that you have. My motto is basically: How do you eat an elephant? One bite at a time. Be patient. Stay focused. And be a great dad.
I have to go now. Thinking about all of this has... well... I have something stuck in my eyes. Both of them. Weird how that happens.