First off, I just want to applaud you for this idea of introducing kids to platformers. There's so many kids games that are like educational and stuff but I've never seen anything like this. And the fact that the same game can be played in kids and adults mode would probably result in so much parent-child bonding! Kids wanting to play the game, just like their parents!
I also really appreciate that while the game is in kids mode, the story is not "watered down" , like the stuff with the dad talking about his job, all the beer stuff etc. Yes kids might not fully understand that, but it's kinda just showing the world as it is! The dynamic between Emily and her father feels so genuine! It really gives the game charm.
I personally think the voice acting in the kids version, subtitling in the adult version is brilliant! I think you could even add more to it... you mention your target age with kids mode is 4-6 right? Since a lot of kids that age can't quite read yet... I'm not sure they'd be able to understand the signs like "moving platform" or "beach elevator."
The solution...?
What if Emily had some voice acting lines too!
Maybe... you can add the E to interact feature into kids mode but instead of interact, it can be "explain" and Emily explains a little more about the signs/platforming mechanics like "this sign says moving platform. I think it will move were I need to go when I stand on it!" or "I should pass under the crystal after it goes up" ... or maybe even after Emily falls off the edge "ouch! I definitely don't want to get that close to the edge again!" That way kids can really get immersed in learning how to platform, and with Emily's voice, they can relate to her character even more and feel like they're learning alongside her. And for kids who already know how to read, maybe there can be an older kids / younger kids switch that turns "E" on and off!
Also, I love how hardcore adult mode is haha. A genuine challenge! I had a lot of fun with it and definitely intend to go back and finish it.
Really really great work here. Hope the suggestions are useful to you for future developments! I cannot wait to see what's to come for the future of this game. I hope it takes off and inspires a new generation of gamers!
-Sasha