My wife ex gets a pass

Have you talked with her about this?

Not that it is fair but there is a reason her ex is her ex - and it is probably in part to just what you are describing...he does nothing or little to nothing - she realizes that at this point so she has excepted it and does the best she can for her kids. And unfairly she is taking it out on you - when you are doing everything for your "shared" child.

Like Mame said talk to her - but do it away from when this happens - I am guessing she is stressed and wrongly taking it out on you. Talking to her away from the situation when she is calm and not just dealing with the ex - you are likely to get someone that can speak reasonably then.