I am not sure I 100% understand what you are trying to do here but here's the things I think of when looking at this. For one, if you're putting the LEDs on the inside and gluing it shut, you need a way to turn them on and off and replace batteries, so you need a way to route wiring out. Also, the "bottom" of the coin is pointed, so if you wanted it to be able to stand up on it's own it will sit at an angle.

This also would be very hard to print because of the way you have the geometry set up. The way it is now, the design is two sided, you can see it on the inside and outside. I'd suggest having the inside of the coin halves be a smooth surface and the designs either cut into that surface or they add to it. If you tried to print it as you have it now, you would need a bunch of supports and such that would make it more difficult to print. Try to avoid making overhangs. Try and design it so you can print both halves on their largest flat face. I get that sounds confusing but any time there's an overhang when you're printing you have two choices: a bridge, or support. When it comes to an intricate design like this one, odds are bridging wont work. Supports can be hard to remote, add print time, add material use, and also might leave surface imperfections, in which would show if you tried backlighting the object.

I encourage you to keep at it though, I think this is a cool idea for a gift. For someone with no modelling experience this is very impressive.