I also have young kiddos and made a Youngling Edition of ESB for them. Need to find time for a ROTJ Youngling edition.

Anyway, I think strategic cuts that remove the more intense elements would make the movie PG. Vader choked out the captain in ANH and Luke’s aunt and uncle were shown as burnt skeletons. I think those scenes, especially the latter, are more intense than most things in TFA.

I’d recommend the following:
-Cut away or remove Lor’s death
-Cut away or remove the village massacre
-Tone down Poe’s interrogation scene
-Minimize on screen fatalities throughout
-Cursing isn’t terribly hard to edit out, my Heir to the Force edit removes it.
-Remove Finn skewering the stormtrooper and some of the more in your face deaths during the Takodana scene.
-You could get creative and have a stormtrooper shoot Han to lessen the creep out factor, but you’d lose the impact if the scene and plot point of the two movies thus far.
-Leaving in Ren’s tantrums may actually make the movie lighter for a kid.
-Not sure if you can do anything about Ren vs Kylo