First, you need to consider that there is no "theoretical physics" per se. Rather, for each branch of physics (condensed matter, materials, optics, atoms&molecules/chemical, biological, particle physics, cosmology,...) there are experimental and theoretical ways to look at them. Each of them has experimentalists and theorists (and the people within a field talk more to each other than theorists of different fields!). The problem now is that while almost all theoretical physics is using large amounts of math, the concrete subfields of math can vary widely between the branches (apart from the basics). And you will only learn what you really need to know once you start working in the field.
I personally consider obtaining a double degree rather pointless; it is much more effective to put the time you'd put into this additional degree into studying your actual field of work. While doing that, you of course need to pick up all the mathematical/programming/chemical/engineering/biology/whatever expertise you require. But the difference is that in this case you *know* what you need to learn, and why, and you're not just studying random stuff.