Once they make the 3 weeks are they pretty much safe, or would the jostling of moving and transporting them in my brother's car increase the likelihood of explosion?
It's more about when you bottle. If you bottle when your gravity is TOO high, say 1.018+ for normal ale's, you could have bottle bombs because you are putting more sugar in the bottle for the yeast to eat (priming sugar), creating another mini-fermentation. 3 weeks bottle conditioning is good, but 4-5 is even better!
If you are worried, chill one down and carefully pop it open. If it spews like a geyser or acts like a shaken can of suds it might be a little overcarbed.