What has worked for us is to minimize time in the morning, mostly due to laziness and trying to sleep in as much as possible. Bath the night before and prep lunch ahead of time. Basically the morning just consists of getting dressed and brushing teeth, before we’re out the door. The way I think about it you’re moving so fast, you don’t let them have time to focus on anything other than getting out of the house.

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.