Ive installed over 5 upgraded sway bars on different vehicles and it has never made a car more stiff, only better on turns. CRV has some bad body roll...but as do other suv's in the the compact segment.Keep in mind that a higher performance sway bar would stiffen up the ride. Personally I find the CR-V is pretty controlled in this area and almost matches the class leading CX-5 while being more comfortable. Its a trade-off you might live with considering a new born would probably prefer smoothness over extreme cornering capability.
Juilt -
The civic and crv shares the same sway bars. Look up aftermarket sway bars from current gen civic. It should bolt right up.