She does use "we" and "us" more often than the average mom complaining about childcare, and grudgingly implies that Dad sometimes does the Friday pickup! She objects that he's not conveying her complaints to Corey's mom but given the complaints I probably wouldn't either if I were married to her.

You're probably right, and he's almost certainly not doing his fair share, but it also seems very likely that she's so self-absorbed she wouldn't think to mention anything he does.