Perhaps. Maybe she thinks they're exaggerating? God knows I only believe half of what comes out of my ex's mouth, and our relationship isn't half as acrimonious...Again, she really truly may simply see this as you trying to control her time, with her child, as a means of keeping your hands on him while he's gone, etc.
Initially, my husband didn't even tell her how we were approaching the assignment at home, to avoid sounding like he wanted to "control" how she handled it. We made sure DSS had the outline he'd worked on, on his laptop, which he took to his Mom's. But if she approached things differently, fine - as long as it got done.
I'm sure she's not the only divorced parent with this type of attitude. But it's not defensible. The kids should be the first priority, not the pettiness.