Gerry, I really feel for you. This sounds just like me and my son's father. The amount of falling out, being stuck in the middle, really is stressful, isn't it. You sound like you are miles ahead of your ex and in the words of my son's psychiatrist - he has his head in the sand. She thinks many men ( not all) have this tendency with anxiety and depression, especially in their sons.
My son's psychiatrist believes that my ex might never see the anxiety for what it is, and believes we just have to keep working around that, as it is his problem, not ours.
My son's father ,like yours, says my son is just putting it on,being lazy. It is crazy, isn't it. It is not wanting to face the reality that this is serious.

Sorry I don't have all the answers on this. I still plough on as I have been told to follow my gut feeling. What can help...if your sons can have the courage, is for them to explain to their dad what they are experieNing. Again, our psychiatrist has told my son to do this and not always try and make me give reasons and explanations. This isn't easy but recently my son emailed his dad (at my request) and explained how he just couldn't do school any more and how bad he felt at school etc. it took the pressure off me and he responded better to my son than had I emailed. Perhaps your sons could do the same thing?

It is too easy for people to blame. You are doing all you can and it can never boil down to your sons being lazy or you being soft.
So stay strong and try not to let their father drag you down. Try to stand your ground or refer him to information he can read on-line.
My ex also hates the psychiatrist, says she does nothing and is just saying and doing what my son wants her to say! Your ex's opinion of camhs sounds similar. Let their father know that you are not alone and that there are lots of parents out there struggling with anxiety and depression and it has to be take seriously as it has to be addressed long term with either medication,small steps, or cbt. If their father ignores this he is not helping them, which of course you have probably told him till you are blue in the face!
Stand tall. You are a good mum in very trying circumstances.
Do something nice for yourself today...
Linda