Looks like you're off to a good start. I'd make a couple suggestions:
First: Dude. Pages. Your schematic is very hard to follow. You can make a hierarchical schematic with multiple pages and actually draw the signal path between them.
The THS6022 is expensive, and it's a dual package with decent power handling. Don't chain them - you're wasting the capacity of the first one. Parallel them instead (each with its own 100 ohm resistor to the output rather than a single 50 ohm termination), which will be much easier on them thermally. If you still need another amplifier for voltage gain, use a cheaper one. I'm not sure about it achieving 20V p-p at 45 MHz**. That's not a trivial task, but it's a pretty good amplifier. I'd just say you should get one and try.
If I were you, I'd be looking into building this on a four-layer PCB. They've become quite affordable lately, and if you want good signal integrity, the good, solid grounding will be a good friend. Power distribution will be much easier too. You could definitely do this on a double-layer board, but I wouldn't find it worth the effort.
As for powering the -13V rail: it's usually going to be less efficient to chain power supplies. However, if you want to support a wide range of input voltages (yes, a discharging battery can count), it could be easier to design just one wide-range DC-DC converter, and then power the rest off the fixed output of that. Your choice.
Quick warning: Watch out, you've got the same pin numbers for both halves of the THS6022.
**Edit: Yeah, it won't do it. Slew rate is 1900V/µs. The maximum slew rate of a 45 MHz signal at 20 Vp-p is (20/2)*2*pi*(45 MHz) = 2800V/µs. You could get 20Vp-p up to almost 30 MHz though, and maybe just drop off the maximum amplitude to 10Vp-p at 45 MHz. I doubt you'd need such a large amplitude at such a high frequency.