Parenting

Is she sleeping in her own room yet or still with you? We transitioned to being in their own room at around the 9 month mark, and that helped a lot. Before then, sleeping was a struggle, and the sleep training really helped around this time. Maybe consider this sooner rather than later if it's this much of a problem.

With regard to the playing in the middle of the night, I'd just cut that and endure the whining for a few days until she realizes that she can't play at night.

Assuming you're bottle feeding, if you and your partner can adjust your sleep schedules to compensate for the 2 hour wakes, that could at least sort out your sanity. For example, if one person went to bed from 10pm - 7am and the other stayed up later and slept from 1am - 9am, then ideally the later sleeper could handle any wakes until 1am. The early sleeper could take the 3am wake, and the later sleeper could do the 5am wake. This way everyone gets about two 4h stretches at a time, and can get a full REM cycles.