I live in Utah and have spent copious time in all of these parks.
@GroveDiesel covered things pretty well. The only things I would add...
1) I would try your best to do more than a mile of the Narrows if you can coax the family into it. The scenery only gets better the further you go in and at about mile 2 (where Orderville Canyon splits off) is where the REALLY REALLY amazing stuff starts.
2) With one day in Arches and a family that are not big hikers I think Landscape + Windows backside + Delicate Arch might be too much for them. Delicate Arch doesn't look like much on paper (1.5mi, 500 ft elevation gain) but it is very exposed to the heat and a grind. You definitely don't want everyone to be too tired to do that one because it is a must see. I would do that area first personally (it is not far from Windows/Double Arch area) and then see if the family still has enough in the tank for Landscape Arch. Don't get me wrong Landscape Arch is very cool, but if something on this trip is worth pushing your family beyond the amount of hiking they want to do it's the Narrows, not Landscape Arch.
3) Emerald Pools 2nd and 3rd pool are cool. 3rd involves a giant waterfall. It is not going to be as cool as the hikes we mentioned above and it is a bit of a grind up to the 3rd pool. See how the family feels when they get to pool #1. It's not a must-see but if they're still feeling up to more it is surely worth doing.
4) I wouldn't try and do Arches and Canyonlands on the same day. You really want to give Arches a full day. It looks like you have a whole day for driving from Bryce to Moab, so I would do Canyonlands that evening. Canyonlands is nice in the evening and the highlights are a relatively quick trip, with mostly overlooks (0.3mi to Mesa Arch your longest walk). 4 hour drive + quick Islands in the Sky tour is easily doable in a day, especially if you just do the main drag up to Grand View Point.
5) Definitely recommend star gazing if you can swing it and are there around a new moon. I am a photographer and these are some of my favorite night photography locations in the world. You don't have to go far out of town to get some truly epic dark skies. Canyonlands is Bortles class 1 or 2 but my favorite is actually Zion which isn't quite as dark, but is still super dark and also gets some nice faint reflections from Springdale that illuminate the canyon walls slightly as a nice foreground view amongst the stars.