Hi, chrissy! I'm so sorry your layered soap separated, what a bummer! The good news is that there's no need to trash the soap - you can always remelt it. I have "glued" dried soap together before with clear base, but when I do it, it's usually to glue a small accent piece on top of a bar (like a soap lime wedge on top of my lime soap, for example). I don't know if it would work for putting your layers back together, but it might be worth a try.
If you sprayed well with alcohol between layers, then I agree with soapbuddy that it probably cooled too much. You want the layer to still be warm but have a thick enough skin on it to support the next layer. The way I check to see if a layer is ready is to gently blow on it. If I see ripples, it's not ready yet. And I usually pour around 115-120 degrees to avoid melting the layer below.
It should be fine to alternate white base and clear base as long as you use the same brand of base. I do it all the time. Different brands set up at different rates, so that's why they say to use the same brand for the whole project. The base you find at the craft store isn't as high quality as Bramble Berry's, in my opinion, and it seems to set up faster.
If you have the patience, you could try to cut the layers apart, remelt, and remold. I've done that before.
Good luck! I hope you can salvage it.