el-ahrairah I would be concerned for the kid too, it sounds like she's living with quite a lot of disruption and possibly not having her needs met in the most effective way. It's hard, people live in different ways, one parent's boundaries may not be another. Do you ever see them together? Do you see the child, does she look well looked after (clean clothes, not hungry etc.), is there interaction between them?
Also, I suppose it depends what time you two go to bed

If you're flaking out at 8.30pm every night that wouldn't be so unusual to have a small child making noise...