Dad is most definitely not Spector + YB, but likely one or the other. Pairing to Ivory should confirm which he is unless you get terrible odds and miss the ALS all together. I don't think Mom has Fire, as she is pretty dark, and Fire should help her hold her color.
As far the reason OS are so different looking, could be one got Specter/YB and the other didn't, could be one didn't actually get Mojave, could just be variation, as Spider can vary wildly in appearance without other morph differences. I would lean towards 1 not having any Specter/YB, and 2 does being the reason given not just the difference in color, but also the dorsal pattern having more of a stripe appearance in the back half where 1 mostly has very broken up dorsal pattern everywhere but the front 1/3 or so. Spiders don't tend to usually get that much striping without help from another morph.
Hope that helps.