Inconsistent bedtimes between houses - killing me

At my place I'm doing 8:30pm bedtime for my 6yo. At mom's house apparently he's going to bed at 10pm sometimes. Kid is exhausted, cranky, harder to manage when he comes back to me. I've tried talking to my ex about it being confusing for him but she says "he goes down when he's ready and I'm not fighting him."

Do I just accept that he has different rules at different places or is this something worth pushing back on?