I live in Brooklyn and have two kids. When I was pregnant with our first, we were living in a large studio apartment. We stayed there until the baby was 1 years old, before moving into a two bedroom. It's absolutely possible and we did not find it difficult. Our baby was a pretty champion sleeper, which helped. I would defer any decisions until the baby is here, and encourage you to stay in your current apartment at least for the first year. Ground level is also a huge benefit because of the stroller. Fwiw, our baby slept in a pack & play for the first year for space reasons, and she is a happy and healthy 5 year old today.
That being said, I would not have wanted my mom to be sleeping at our apartment 4 nights a week. It would have been very tough on us and also on her. If she's sleeping in the living room, she may not feel comfortable telling you to essentially go to bed so she can sleep, and you have nowhere to hang out other than the bedroom. Have you spoken to her about this plan? A 30 minute commute does not seem that long, especially if you and your wife are able to shift your work schedules so one of you starts earlier and ends earlier, thereby reducing the amount of time that grandma would have to be on duty. Luckily there is plenty of time before any of this will actually come into play, but it bears thinking about.
Congratulations and good luck! (Also, the 3K program is not universal and is in fact getting cut by Adams, so I wouldn't necessarily rely on it!)