So basically this is a Firefly-like setup - multiple planets in a solar system but no extra-solar activity?
I don't think speed is the problem here - no matter what, if you've got interplanetary travel that is is relatively quick (ie, a week or two) then there's always going to be the possibility of leaving the solar system. You can't change that, and you could perhaps use it as a hook of some kind.
The biggest impediments to leaving the solar system would be calculating trajectory and needing supplies.
Even with multiple planets, a good captain is going to want to conserve supplies - fuel, oxygen if you don't have some sort of scrubber system, food and other necessities, water, and I'm sure you can come up with more. So calculating a trajectory that not only avoids solar bodies (asteroids, moons, the sun, other planets, etc) but gets you from X to Y in the fastest and easiest path is no small feat even in one solar system. You can semi-handwave that plotting that course to an unknown solar system is all but impossible, especially without any sort of charts. Not to mention it would take decades, and no sure chance of finding anything.
The other problem of course is supply. You would need such an enormous amount of supplies to make that trip it would be rediculous to try and calculate the logistics of it. You would need vast stores of supplies and since that's mass, even more vast supplies of fuel - only governments, corporations, and the obscenely rich will even have the resources to attempt it - and why would they bother?
So, really the speed issue isn't really an issue at all. I wouldn't worry about it.
As for atmospheric stuff - as someone said above, spaceships don't have to worry about friction. The largest spaceships will be unlikely to be able to land on a planet (think Enterprise, Galactica, and other large-ish ships). Smaller ships might be able to navigate both atmosphere and space, but atmosphere is going to be much clumsier and more stressful on the ship unless it is specifically designed to do both (Serenity, Raptors, Shuttles, Puddle Jumpers) - and even then, atmospheric craft (ie fighters, bombers) will be more than a match for it.
[edit]Now I really want to play StarDrive! Even a PbP game!
Speaking of though, I'm sure GURPS has a few books on the issue. I'd recommend checking out StarDrive and Alternity if you can find them - they sound like they might be a good reference. Also, you can always Wikipedia our solar system and nearby ones (Alpha Centauri, Betelguese) to get some idea of distances and speeds.