The most tempting about the Nikon is the sensor size. But, for me, I just gave my aps-c camera away, because I admitted, wonderful as it is, I left it home all the time since I got my type 1 rx100.
the 2 Nikon lenses are fairly dark, so shutter speed for motion (anything, and future baby) will be more of an issue with Nikon. Brighter lenses are big and costly as you know.
I vote for the Stylus 1 (or 1s if you cannot find an original 1 at a lower price). Upgrade firmware of 1 equals 1s, (except very minor styling change). It is a remarkable camera IMO. I had Sony's type 1 RX10, 24-200, sold it, got the Stylus 1, no regrets.
It starts at 28mm, I would prefer 24mm as you mentioned. It is a constant f2.8 to 300mm, which is remarkable.
All that fits easily in a Jacket Pocket or small belt/shoulder case.
Oly has 2X which doubles optical using an in-camera crop and in-camera up-scaling, it is quite good, here is 2X600mm, handheld, OOC Jpeg, no PP. Now 28-600mm in your small case. It is for 'occassional, effortless, good enough' use.
Oly's colors are quite nice. The camera has threads, for two optional conversion lenses, a wide angle, giving optical of about 22mm, and a tele, giving optical to 510mm and 1,024mm using 2X. It maintains f2.8 to 510/1,024. They can be added later of course.
Anything can break, so I recommend a pair of cameras, especially for travel. I pair mine with the smaller, brighter, low light motion miniature monster rx100m3, type 1 sensor in your pants pocket. That can be added later of course, I would start with the Stylus 1 because of the travel mentioned.
If you started with the rx100m3, you get 24-70mm, type 1, 20mp, which crops well, so it's reach can be extended. It is incredible to have it with you always. Then, like I did, add the Stylus 1 later as the 2nd camera.
Except for low light/motion (sony is f1.8), it doesn't matter to me which camera I have left home, they both, despite sensor size differences, give excellent results. Oly is ok to ISO 1,600. Sony can go much higher ISO, or, give much lower ISO is the same situation.
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Elliott