On the flash.
MOST top tier defensive loads these days incorporate a flash reduction component in the propellant. The specialty loadings for short barreled handguns use a faster burning propellant to increase velocity through more complete combustion and in the process reduce muzzle flash from unburnt propellant.
Realisticly, muzzle flash is not an issue anymore than muzzle blast when under stress, though if you do take the time to train in low light, you will learn to use the muzzle flash to index the front sight and correct on the next.
The utility of a 2" barrel is it's ease of portability.
The tradeoff is contol, and recoil due to physics.
Mechanical accuracy is unrelated.
Long story short, it is more difficult to make hits with a short barreled sidearm, and markedly so when under stress.
Seeing as how it will be a "House gun" and not concealed, it's primary attribute is not needed, and is a detriment to it's primary function.
A good used std. 4" .38spl Revolver like the old M10, has many advantages over the little J frame, and thanks to a gazillion of 'em bieng out there, cost less as they aren't competing for the concealed carry market.
J-frames are neat little snots that slide nicely into a jacket pocket or dissapear in a belt slide under a loose sweater.
But if you aren't going to carry the thing, it would be wise to consider the disadvantages that come with it's concealability.
Then again a J-frame might justify a bigger brother or two.
It's been known to happen that way.
Just My .02
I wish ya luck.