Is it usual for a PhD thesis to have two distinct subjects?
Option 1. At least in computer science, it happens often (but not always) that someone works on several somewhat disjoint but somewhat related problems. It's all about the glue and the story; if you can sell the cohesiveness of the thesis in the abstract and introduction, you're golden. Be upfront about the fact that there may be some disjoint problems, but try to find and highlight the unifying themes. 

Here's a quote my advisor always tells us which has relevance to this: "all wells, when dug deep enough, lead to the same water source."