If Yavin/Moon relationship is anything like Jupiter/Earth size relationship, then the planet Yavin is about 1,300 times bigger.
I'm perfectly willing to beleive that "the power to blow up a planet" means the power to blow up a rocky planet, roughly similar to Alderaan, not the power to blow up ANY planet.
I'll also buy that the DS needs to recharge. I'll buy that it's too close to the gas giant. It all makes sense. What I won't buy is that all the characters are just too stupid to do it.
I feel that 2/3 of complaints about the SW movies are that a fan invents a rule that's not in the movie, then complains that the movie doesn't follow it.